WorldWideScience

Sample records for monotonically convergent algorithm

  1. Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Chakkrid Klin-eam

    2009-01-01

    Full Text Available We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space.

  2. New concurrent iterative methods with monotonic convergence

    Energy Technology Data Exchange (ETDEWEB)

    Yao, Qingchuan [Michigan State Univ., East Lansing, MI (United States)

    1996-12-31

    This paper proposes the new concurrent iterative methods without using any derivatives for finding all zeros of polynomials simultaneously. The new methods are of monotonic convergence for both simple and multiple real-zeros of polynomials and are quadratically convergent. The corresponding accelerated concurrent iterative methods are obtained too. The new methods are good candidates for the application in solving symmetric eigenproblems.

  3. Super-Relaxed ( -Proximal Point Algorithms, Relaxed ( -Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions

    Directory of Open Access Journals (Sweden)

    Agarwal RaviP

    2009-01-01

    Full Text Available We glance at recent advances to the general theory of maximal (set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed ( -proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion of maximal ( -monotonicity. Investigations highlighted in this communication are greatly influenced by the celebrated work of Rockafellar (1976, while others have played a significant part as well in generalizing the proximal point algorithm considered by Rockafellar (1976 to the case of the relaxed proximal point algorithm by Eckstein and Bertsekas (1992. Even for the linear convergence analysis for the overrelaxed (or super-relaxed ( -proximal point algorithm, the fundamental model for Rockafellar's case does the job. Furthermore, we attempt to explore possibilities of generalizing the Yosida regularization/approximation in light of maximal ( -monotonicity, and then applying to first-order evolution equations/inclusions.

  4. Application of a repetitive process setting to design of monotonically convergent iterative learning control

    Science.gov (United States)

    Boski, Marcin; Paszke, Wojciech

    2015-11-01

    This paper deals with the problem of designing an iterative learning control algorithm for discrete linear systems using repetitive process stability theory. The resulting design produces a stabilizing output feedback controller in the time domain and a feedforward controller that guarantees monotonic convergence in the trial-to-trial domain. The results are also extended to limited frequency range design specification. New design procedure is introduced in terms of linear matrix inequality (LMI) representations, which guarantee the prescribed performances of ILC scheme. A simulation example is given to illustrate the theoretical developments.

  5. Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

    Directory of Open Access Journals (Sweden)

    Ram U. Verma

    2009-01-01

    Full Text Available Based on a notion of relatively maximal (m-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976 on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.

  6. Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks

    Directory of Open Access Journals (Sweden)

    Huisheng Zhang

    2009-01-01

    Full Text Available The batch split-complex backpropagation (BSCBP algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to zero. By adding a moderate condition, the weights sequence itself is also proved to be convergent. A numerical example is given to support the theoretical analysis.

  7. A simple algorithm for computing positively weighted straight skeletons of monotone polygons☆

    Science.gov (United States)

    Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter

    2015-01-01

    We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlog⁡n) time and O(n) space, where n denotes the number of vertices of the polygon. PMID:25648376

  8. A simple algorithm for computing positively weighted straight skeletons of monotone polygons.

    Science.gov (United States)

    Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter

    2015-02-01

    We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where n denotes the number of vertices of the polygon.

  9. Robust Monotonically Convergent Iterative Learning Control for Discrete-Time Systems via Generalized KYP Lemma

    Directory of Open Access Journals (Sweden)

    Jian Ding

    2014-01-01

    Full Text Available This paper addresses the problem of P-type iterative learning control for a class of multiple-input multiple-output linear discrete-time systems, whose aim is to develop robust monotonically convergent control law design over a finite frequency range. It is shown that the 2 D iterative learning control processes can be taken as 1 D state space model regardless of relative degree. With the generalized Kalman-Yakubovich-Popov lemma applied, it is feasible to describe the monotonically convergent conditions with the help of linear matrix inequality technique and to develop formulas for the control gain matrices design. An extension to robust control law design against systems with structured and polytopic-type uncertainties is also considered. Two numerical examples are provided to validate the feasibility and effectiveness of the proposed method.

  10. A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Jinlin Guan

    2013-01-01

    Full Text Available We introduce a new monotone mapping in Banach spaces, which is an extension of the -monotone mapping studied by Nazemi (2012, and we generalize the variational inclusion involving the -monotone mapping. Based on the new monotone mapping, we propose a new proximal mapping which combines the proximal mapping studied by Nazemi (2012 with the mapping studied by Lan et al. (2011 and show its Lipschitz continuity. Based on the new proximal mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.

  11. A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties

    International Nuclear Information System (INIS)

    Huang Zhenghai; Gu Weizhe

    2008-01-01

    In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge, such properties have not appeared in the existing literature for smoothing-type algorithms

  12. Non-Interior Continuation Method for Solving the Monotone Semidefinite Complementarity Problem

    International Nuclear Information System (INIS)

    Huang, Z.H.; Han, J.

    2003-01-01

    Recently, Chen and Tseng extended non-interior continuation smoothing methods for solving linear/ nonlinear complementarity problems to semidefinite complementarity problems (SDCP). In this paper we propose a non-interior continuation method for solving the monotone SDCP based on the smoothed Fischer-Burmeister function, which is shown to be globally linearly and locally quadratically convergent under suitable assumptions. Our algorithm needs at most to solve a linear system of equations at each iteration. In addition, in our analysis on global linear convergence of the algorithm, we need not use the assumption that the Frechet derivative of the function involved in the SDCP is Lipschitz continuous. For non-interior continuation/ smoothing methods for solving the nonlinear complementarity problem, such an assumption has been used widely in the literature in order to achieve global linear convergence results of the algorithms

  13. Monotone piecewise bicubic interpolation

    International Nuclear Information System (INIS)

    Carlson, R.E.; Fritsch, F.N.

    1985-01-01

    In a 1980 paper the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone script C 1 piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm. 4 references, 6 figures, 2 tables

  14. Convergence Performance of Adaptive Algorithms of L-Filters

    Directory of Open Access Journals (Sweden)

    Robert Hudec

    2003-01-01

    Full Text Available This paper deals with convergence parameters determination of adaptive algorithms, which are used in adaptive L-filters design. Firstly the stability of adaptation process, convergence rate or adaptation time, and behaviour of convergence curve belong among basic properties of adaptive algorithms. L-filters with variety of adaptive algorithms were used to their determination. Convergence performances finding of adaptive filters is important mainly for their hardware applications, where filtration in real time or adaptation of coefficient filter with low capacity of input data are required.

  15. Convergence rates and finite-dimensional approximations for nonlinear ill-posed problems involving monotone operators in Banach spaces

    International Nuclear Information System (INIS)

    Nguyen Buong.

    1992-11-01

    The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs

  16. Accelerated convergence of the steepest-descent method for magnetohydrodynamic equilibria

    International Nuclear Information System (INIS)

    Handy, C.R.; Hirshman, S.P.

    1984-06-01

    Iterative schemes based on the method of steepest descent have recently been used to obtain magnetohydrodynamic (MHD) equilibria. Such schemes generate asymptotic geometric vector sequences whose convergence rate can be improved through the use of the epsilon-algorithm. The application of this nonlinear recursive technique to stiff systems is discussed. In principle, the epsilon-algorithm is capable of yielding quadratic convergence and therefore represents an attractive alternative to other quadratic convergence schemes requiring Jacobian matrix inversion. Because the damped MHD equations have eigenvalues with negative real parts (in the neighborhood of a stable equilibrium), the epsilon-algorithm will generally be stable. Concern for residual monotonic sequences leads to consideration of alternative methods for implementing the algorithm

  17. A generalization of Takane's algorithm for DEDICOM

    NARCIS (Netherlands)

    Kiers, Henk A.L.; ten Berge, Jos M.F.; Takane, Yoshio; de Leeuw, Jan

    An algorithm is described for fitting the DEDICOM model for the analysis of asymmetric data matrices. This algorithm generalizes an algorithm suggested by Takane in that it uses a damping parameter in the iterative process. Takane's algorithm does not always converge monotonically. Based on the

  18. Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

    Directory of Open Access Journals (Sweden)

    Kriengsak Wattanawitoon

    2011-01-01

    Full Text Available We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008 and many authors.

  19. Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Watcharaporn Cholamjiak

    2009-01-01

    Full Text Available We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006 and Nakajo and Takahashi (2003.

  20. Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

    Science.gov (United States)

    Sun, Yong; Meng, Zhaohai; Li, Fengting

    2018-03-01

    Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

  1. Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

    KAUST Repository

    Liu, Lulu

    2016-10-26

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

  2. Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

    KAUST Repository

    Liu, Lulu; Keyes, David E.

    2016-01-01

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

  3. Convergence analysis of canonical genetic algorithms.

    Science.gov (United States)

    Rudolph, G

    1994-01-01

    This paper analyzes the convergence properties of the canonical genetic algorithm (CGA) with mutation, crossover and proportional reproduction applied to static optimization problems. It is proved by means of homogeneous finite Markov chain analysis that a CGA will never converge to the global optimum regardless of the initialization, crossover, operator and objective function. But variants of CGA's that always maintain the best solution in the population, either before or after selection, are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent CGA. These results are discussed with respect to the schema theorem.

  4. A new efficient algorithm for computing the imprecise reliability of monotone systems

    International Nuclear Information System (INIS)

    Utkin, Lev V.

    2004-01-01

    Reliability analysis of complex systems by partial information about reliability of components and by different conditions of independence of components may be carried out by means of the imprecise probability theory which provides a unified framework (natural extension, lower and upper previsions) for computing the system reliability. However, the application of imprecise probabilities to reliability analysis meets with a complexity of optimization problems which have to be solved for obtaining the system reliability measures. Therefore, an efficient simplified algorithm to solve and decompose the optimization problems is proposed in the paper. This algorithm allows us to practically implement reliability analysis of monotone systems under partial and heterogeneous information about reliability of components and under conditions of the component independence or the lack of information about independence. A numerical example illustrates the algorithm

  5. Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations

    NARCIS (Netherlands)

    Groenwold, A.A.; Wood, D.W.; Etman, L.F.P.; Tosserams, S.

    2009-01-01

    We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by

  6. Convergence analysis of Chauvin's PCA learning algorithm with a constant learning rate

    International Nuclear Information System (INIS)

    Lv Jiancheng; Yi Zhang

    2007-01-01

    The convergence of Chauvin's PCA learning algorithm with a constant learning rate is studied in this paper by using a DDT method (deterministic discrete-time system method). Different from the DCT method (deterministic continuous-time system method), the DDT method does not require that the learning rate converges to zero. An invariant set of Chauvin's algorithm with a constant learning rate is obtained so that the non-divergence of this algorithm can be guaranteed. Rigorous mathematic proofs are provided to prove the local convergence of this algorithm

  7. Maximum-entropy clustering algorithm and its global convergence analysis

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.

  8. The converged Sn algorithm for nuclear criticality

    International Nuclear Information System (INIS)

    Ganapol, B. D.; Hadad, K.

    2009-01-01

    A new discrete ordinates algorithm to determine the multiplication factor of a 1D nuclear reactor, based on Bengt Carlson's S n method, is presented. The algorithm applies the Romberg and Wynn-epsilon accelerators to accelerate a 1D, one-group S n solution to its asymptotic limit. We demonstrate the feasibility of the Converged Sn (CSn) solution on several one-group criticality benchmark compilations. The new formulation is especially convenient since it enables highly accurate critical fluxes and eigenvalues using the most fundamental transport algorithm. (authors)

  9. A unified framework of descent algorithms for nonlinear programs and variational inequalities

    International Nuclear Information System (INIS)

    Patriksson, M.

    1993-01-01

    We present a framework of algorithms for the solution of continuous optimization and variational inequality problems. In the general algorithm, a search direction finding auxiliary problems is obtained by replacing the original cost function with an approximating monotone cost function. The proposed framework encompasses algorithm classes presented earlier by Cohen, Dafermos, Migdalas, and Tseng, and includes numerous descent and successive approximation type methods, such as Newton methods, Jacobi and Gauss-Siedel type decomposition methods for problems defined over Cartesian product sets, and proximal point methods, among others. The auxiliary problem of the general algorithm also induces equivalent optimization reformulation and descent methods for asymmetric variational inequalities. We study the convergence properties of the general algorithm when applied to unconstrained optimization, nondifferentiable optimization, constrained differentiable optimization, and variational inequalities; the emphasis of the convergence analyses is placed on basic convergence results, convergence using different line search strategies and truncated subproblem solutions, and convergence rate results. This analysis offer a unification of known results; moreover, it provides strengthenings of convergence results for many existing algorithms, and indicates possible improvements of their realizations. 482 refs

  10. A Rapid Convergent Low Complexity Interference Alignment Algorithm for Wireless Sensor Networks

    Directory of Open Access Journals (Sweden)

    Lihui Jiang

    2015-07-01

    Full Text Available Interference alignment (IA is a novel technique that can effectively eliminate the interference and approach the sum capacity of wireless sensor networks (WSNs when the signal-to-noise ratio (SNR is high, by casting the desired signal and interference into different signal subspaces. The traditional alternating minimization interference leakage (AMIL algorithm for IA shows good performance in high SNR regimes, however, the complexity of the AMIL algorithm increases dramatically as the number of users and antennas increases, posing limits to its applications in the practical systems. In this paper, a novel IA algorithm, called directional quartic optimal (DQO algorithm, is proposed to minimize the interference leakage with rapid convergence and low complexity. The properties of the AMIL algorithm are investigated, and it is discovered that the difference between the two consecutive iteration results of the AMIL algorithm will approximately point to the convergence solution when the precoding and decoding matrices obtained from the intermediate iterations are sufficiently close to their convergence values. Based on this important property, the proposed DQO algorithm employs the line search procedure so that it can converge to the destination directly. In addition, the optimal step size can be determined analytically by optimizing a quartic function. Numerical results show that the proposed DQO algorithm can suppress the interference leakage more rapidly than the traditional AMIL algorithm, and can achieve the same level of sum rate as that of AMIL algorithm with far less iterations and execution time.

  11. A Rapid Convergent Low Complexity Interference Alignment Algorithm for Wireless Sensor Networks.

    Science.gov (United States)

    Jiang, Lihui; Wu, Zhilu; Ren, Guanghui; Wang, Gangyi; Zhao, Nan

    2015-07-29

    Interference alignment (IA) is a novel technique that can effectively eliminate the interference and approach the sum capacity of wireless sensor networks (WSNs) when the signal-to-noise ratio (SNR) is high, by casting the desired signal and interference into different signal subspaces. The traditional alternating minimization interference leakage (AMIL) algorithm for IA shows good performance in high SNR regimes, however, the complexity of the AMIL algorithm increases dramatically as the number of users and antennas increases, posing limits to its applications in the practical systems. In this paper, a novel IA algorithm, called directional quartic optimal (DQO) algorithm, is proposed to minimize the interference leakage with rapid convergence and low complexity. The properties of the AMIL algorithm are investigated, and it is discovered that the difference between the two consecutive iteration results of the AMIL algorithm will approximately point to the convergence solution when the precoding and decoding matrices obtained from the intermediate iterations are sufficiently close to their convergence values. Based on this important property, the proposed DQO algorithm employs the line search procedure so that it can converge to the destination directly. In addition, the optimal step size can be determined analytically by optimizing a quartic function. Numerical results show that the proposed DQO algorithm can suppress the interference leakage more rapidly than the traditional AMIL algorithm, and can achieve the same level of sum rate as that of AMIL algorithm with far less iterations and execution time.

  12. Convergence analysis of Chauvin's PCA learning algorithm with a constant learning rate

    Energy Technology Data Exchange (ETDEWEB)

    Lv Jiancheng [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China); Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn

    2007-05-15

    The convergence of Chauvin's PCA learning algorithm with a constant learning rate is studied in this paper by using a DDT method (deterministic discrete-time system method). Different from the DCT method (deterministic continuous-time system method), the DDT method does not require that the learning rate converges to zero. An invariant set of Chauvin's algorithm with a constant learning rate is obtained so that the non-divergence of this algorithm can be guaranteed. Rigorous mathematic proofs are provided to prove the local convergence of this algorithm.

  13. Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Juguo Su

    2012-01-01

    Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

  14. Computation of Optimal Monotonicity Preserving General Linear Methods

    KAUST Repository

    Ketcheson, David I.

    2009-07-01

    Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.

  15. Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

    Science.gov (United States)

    Li, Xiao; Scaglione, Anna

    2013-11-01

    The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

  16. Simulating quantum search algorithm using vibronic states of I2 manipulated by optimally designed gate pulses

    International Nuclear Information System (INIS)

    Ohtsuki, Yukiyoshi

    2010-01-01

    In this paper, molecular quantum computation is numerically studied with the quantum search algorithm (Grover's algorithm) by means of optimal control simulation. Qubits are implemented in the vibronic states of I 2 , while gate operations are realized by optimally designed laser pulses. The methodological aspects of the simulation are discussed in detail. We show that the algorithm for solving a gate pulse-design problem has the same mathematical form as a state-to-state control problem in the density matrix formalism, which provides monotonically convergent algorithms as an alternative to the Krotov method. The sequential irradiation of separately designed gate pulses leads to the population distribution predicted by Grover's algorithm. The computational accuracy is reduced by the imperfect quality of the pulse design and by the electronic decoherence processes that are modeled by the non-Markovian master equation. However, as long as we focus on the population distribution of the vibronic qubits, we can search a target state with high probability without introducing error-correction processes during the computation. A generalized gate pulse-design scheme to explicitly include decoherence effects is outlined, in which we propose a new objective functional together with its solution algorithm that guarantees monotonic convergence.

  17. Global Convergence of the EM Algorithm for Unconstrained Latent Variable Models with Categorical Indicators

    Science.gov (United States)

    Weissman, Alexander

    2013-01-01

    Convergence of the expectation-maximization (EM) algorithm to a global optimum of the marginal log likelihood function for unconstrained latent variable models with categorical indicators is presented. The sufficient conditions under which global convergence of the EM algorithm is attainable are provided in an information-theoretic context by…

  18. A Penalization-Gradient Algorithm for Variational Inequalities

    Directory of Open Access Journals (Sweden)

    Abdellatif Moudafi

    2011-01-01

    Full Text Available This paper is concerned with the study of a penalization-gradient algorithm for solving variational inequalities, namely, find x̅∈C such that 〈Ax̅,y-x̅〉≥0 for all y∈C, where A:H→H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ:H→R  ∪  {+∞} which acts as a penalization function with respect to the constraint x̅∈C, and a penalization parameter βk, we consider an algorithm which alternates a proximal step with respect to ∂Ψ and a gradient step with respect to A and reads as xk=(I+λkβk∂Ψ-1(xk-1-λkAxk-1. Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing the multivalued operator by its Yosida approximate which is always Lipschitz continuous.

  19. A globally convergent MC algorithm with an adaptive learning rate.

    Science.gov (United States)

    Peng, Dezhong; Yi, Zhang; Xiang, Yong; Zhang, Haixian

    2012-02-01

    This brief deals with the problem of minor component analysis (MCA). Artificial neural networks can be exploited to achieve the task of MCA. Recent research works show that convergence of neural networks based MCA algorithms can be guaranteed if the learning rates are less than certain thresholds. However, the computation of these thresholds needs information about the eigenvalues of the autocorrelation matrix of data set, which is unavailable in online extraction of minor component from input data stream. In this correspondence, we introduce an adaptive learning rate into the OJAn MCA algorithm, such that its convergence condition does not depend on any unobtainable information, and can be easily satisfied in practical applications.

  20. A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

    Directory of Open Access Journals (Sweden)

    Zhijun Luo

    2014-01-01

    Full Text Available A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

  1. A Convergent Differential Evolution Algorithm with Hidden Adaptation Selection for Engineering Optimization

    Directory of Open Access Journals (Sweden)

    Zhongbo Hu

    2014-01-01

    Full Text Available Many improved differential Evolution (DE algorithms have emerged as a very competitive class of evolutionary computation more than a decade ago. However, few improved DE algorithms guarantee global convergence in theory. This paper developed a convergent DE algorithm in theory, which employs a self-adaptation scheme for the parameters and two operators, that is, uniform mutation and hidden adaptation selection (haS operators. The parameter self-adaptation and uniform mutation operator enhance the diversity of populations and guarantee ergodicity. The haS can automatically remove some inferior individuals in the process of the enhancing population diversity. The haS controls the proposed algorithm to break the loop of current generation with a small probability. The breaking probability is a hidden adaptation and proportional to the changes of the number of inferior individuals. The proposed algorithm is tested on ten engineering optimization problems taken from IEEE CEC2011.

  2. Convergence of SART + OS + TV iterative reconstruction algorithm for optical CT imaging of gel dosimeters

    International Nuclear Information System (INIS)

    Du, Yi; Yu, Gongyi; Xiang, Xincheng; Wang, Xiangang; De Deene, Yves

    2017-01-01

    Computational simulations are used to investigate the convergence of a hybrid iterative algorithm for optical CT reconstruction, i.e. the simultaneous algebraic reconstruction technique (SART) integrated with ordered subsets (OS) iteration and total variation (TV) minimization regularization, or SART+OS+TV for short. The influence of parameter selection to reach convergence, spatial dose gradient integrity, MTF and convergent speed are discussed. It’s shown that the results of SART+OS+TV algorithm converge to the true values without significant bias, and MTF and convergent speed are affected by different parameter sets used for iterative calculation. In conclusion, the performance of the SART+OS+TV depends on parameter selection, which also implies that careful parameter tuning work is required and necessary for proper spatial performance and fast convergence. (paper)

  3. A Superlinearly Convergent O(square root of nL)-Iteration Algorithm for Linear Programming

    National Research Council Canada - National Science Library

    Ye, Y; Tapia, Richard A; Zhang, Y

    1991-01-01

    .... We demonstrate that the modified algorithm maintains its O(square root of nL)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for nondegenerate problems...

  4. On the Convergence of Iterative Receiver Algorithms Utilizing Hard Decisions

    Directory of Open Access Journals (Sweden)

    Jürgen F. Rößler

    2009-01-01

    Full Text Available The convergence of receivers performing iterative hard decision interference cancellation (IHDIC is analyzed in a general framework for ASK, PSK, and QAM constellations. We first give an overview of IHDIC algorithms known from the literature applied to linear modulation and DS-CDMA-based transmission systems and show the relation to Hopfield neural network theory. It is proven analytically that IHDIC with serial update scheme always converges to a stable state in the estimated values in course of iterations and that IHDIC with parallel update scheme converges to cycles of length 2. Additionally, we visualize the convergence behavior with the aid of convergence charts. Doing so, we give insight into possible errors occurring in IHDIC which turn out to be caused by locked error situations. The derived results can directly be applied to those iterative soft decision interference cancellation (ISDIC receivers whose soft decision functions approach hard decision functions in course of the iterations.

  5. Monotone methods for solving a boundary value problem of second order discrete system

    Directory of Open Access Journals (Sweden)

    Wang Yuan-Ming

    1999-01-01

    Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

  6. Exponentially Convergent Algorithms for Abstract Differential Equations

    CERN Document Server

    Gavrilyuk, Ivan; Vasylyk, Vitalii

    2011-01-01

    This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which

  7. Robust consensus algorithm for multi-agent systems with exogenous disturbances under convergence conditions

    Science.gov (United States)

    Jiang, Yulian; Liu, Jianchang; Tan, Shubin; Ming, Pingsong

    2014-09-01

    In this paper, a robust consensus algorithm is developed and sufficient conditions for convergence to consensus are proposed for a multi-agent system (MAS) with exogenous disturbances subject to partial information. By utilizing H∞ robust control, differential game theory and a design-based approach, the consensus problem of the MAS with exogenous bounded interference is resolved and the disturbances are restrained, simultaneously. Attention is focused on designing an H∞ robust controller (the robust consensus algorithm) based on minimisation of our proposed rational and individual cost functions according to goals of the MAS. Furthermore, sufficient conditions for convergence of the robust consensus algorithm are given. An example is employed to demonstrate that our results are effective and more capable to restrain exogenous disturbances than the existing literature.

  8. Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model.

    Science.gov (United States)

    Laamiri, Imen; Khouaja, Anis; Messaoud, Hassani

    2015-03-01

    In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS). Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  9. A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints

    International Nuclear Information System (INIS)

    Jian Jinbao; Li Jianling; Mo Xingde

    2006-01-01

    This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998),5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported

  10. Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria

    Directory of Open Access Journals (Sweden)

    Lu-Chuan Ceng

    2014-01-01

    Full Text Available We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.

  11. A Local and Global Search Combined Particle Swarm Optimization Algorithm and Its Convergence Analysis

    Directory of Open Access Journals (Sweden)

    Weitian Lin

    2014-01-01

    Full Text Available Particle swarm optimization algorithm (PSOA is an advantage optimization tool. However, it has a tendency to get stuck in a near optimal solution especially for middle and large size problems and it is difficult to improve solution accuracy by fine-tuning parameters. According to the insufficiency, this paper researches the local and global search combine particle swarm algorithm (LGSCPSOA, and its convergence and obtains its convergence qualification. At the same time, it is tested with a set of 8 benchmark continuous functions and compared their optimization results with original particle swarm algorithm (OPSOA. Experimental results indicate that the LGSCPSOA improves the search performance especially on the middle and large size benchmark functions significantly.

  12. Weak and Strong Convergence of an Algorithm for the Split Common Fixed-Point of Asymptotically Quasi-Nonexpansive Operators

    Directory of Open Access Journals (Sweden)

    Yazheng Dang

    2013-01-01

    Full Text Available Inspired by the Moudafi (2010, we propose an algorithm for solving the split common fixed-point problem for a wide class of asymptotically quasi-nonexpansive operators and the weak and strong convergence of the algorithm are shown under some suitable conditions in Hilbert spaces. The algorithm and its convergence results improve and develop previous results for split feasibility problems.

  13. A proximal point algorithm with generalized proximal distances to BEPs

    OpenAIRE

    Bento, G. C.; Neto, J. X. Cruz; Lopes, J. O.; Soares Jr, P. A.; Soubeyran, A.

    2014-01-01

    We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequences generated by the algorithm. This class of problems is very interesting because it covers mathematical programs and optimization problems under equilibrium constraints. As an application, we consider the problem of the stability and change dyna...

  14. A Low Delay and Fast Converging Improved Proportionate Algorithm for Sparse System Identification

    Directory of Open Access Journals (Sweden)

    Benesty Jacob

    2007-01-01

    Full Text Available A sparse system identification algorithm for network echo cancellation is presented. This new approach exploits both the fast convergence of the improved proportionate normalized least mean square (IPNLMS algorithm and the efficient implementation of the multidelay adaptive filtering (MDF algorithm inheriting the beneficial properties of both. The proposed IPMDF algorithm is evaluated using impulse responses with various degrees of sparseness. Simulation results are also presented for both speech and white Gaussian noise input sequences. It has been shown that the IPMDF algorithm outperforms the MDF and IPNLMS algorithms for both sparse and dispersive echo path impulse responses. Computational complexity of the proposed algorithm is also discussed.

  15. Monotonism.

    Science.gov (United States)

    Franklin, Elda

    1981-01-01

    Reviews studies on the etiology of monotonism, the monotone being that type of uncertain or inaccurate singer who cannot vocally match pitches and who has trouble accurately reproducing even a familiar song. Neurological factors (amusia, right brain abnormalities), age, and sex differences are considered. (Author/SJL)

  16. Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

    Science.gov (United States)

    Zhao, Ying; Shi, Luoyi

    2017-01-01

    This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.

  17. Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems

    International Nuclear Information System (INIS)

    Stipanović, Dušan M.; Tomlin, Claire J.; Leitmann, George

    2012-01-01

    In this paper the problem of accomplishing multiple objectives by a number of agents represented as dynamic systems is considered. Each agent is assumed to have a goal which is to accomplish one or more objectives where each objective is mathematically formulated using an appropriate objective function. Sufficient conditions for accomplishing objectives are derived using particular convergent approximations of minimum and maximum functions depending on the formulation of the goals and objectives. These approximations are differentiable functions and they monotonically converge to the corresponding minimum or maximum function. Finally, an illustrative pursuit-evasion game example with two evaders and two pursuers is provided.

  18. Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems

    Energy Technology Data Exchange (ETDEWEB)

    Stipanovic, Dusan M., E-mail: dusan@illinois.edu [University of Illinois at Urbana-Champaign, Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering (United States); Tomlin, Claire J., E-mail: tomlin@eecs.berkeley.edu [University of California at Berkeley, Department of Electrical Engineering and Computer Science (United States); Leitmann, George, E-mail: gleit@berkeley.edu [University of California at Berkeley, College of Engineering (United States)

    2012-12-15

    In this paper the problem of accomplishing multiple objectives by a number of agents represented as dynamic systems is considered. Each agent is assumed to have a goal which is to accomplish one or more objectives where each objective is mathematically formulated using an appropriate objective function. Sufficient conditions for accomplishing objectives are derived using particular convergent approximations of minimum and maximum functions depending on the formulation of the goals and objectives. These approximations are differentiable functions and they monotonically converge to the corresponding minimum or maximum function. Finally, an illustrative pursuit-evasion game example with two evaders and two pursuers is provided.

  19. Unordered Monotonicity.

    Science.gov (United States)

    Heckman, James J; Pinto, Rodrigo

    2018-01-01

    This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogenous agents and discrete-valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.

  20. Accuracy, convergence and stability of finite element CFD algorithms

    International Nuclear Information System (INIS)

    Baker, A.J.; Iannelli, G.S.; Noronha, W.P.

    1989-01-01

    The requirement for artificial dissipation is well understood for shock-capturing CFD procedures in aerodynamics. However, numerical diffusion is widely utilized across the board in Navier-Stokes CFD algorithms, ranging from incompressible through supersonic flow applications. The Taylor weak statement (TWS) theory is applicable to any conservation law system containing an evolutionary component, wherein the analytical modifications becomes functionally dependent on the Jacobian of the corresponding equation system flux vector. The TWS algorithm is developed for a range of fluid mechanics conservation law systems including incompressible Navier-Stokes, depth-averaged free surface hydrodynamic Navier-Stokes, and the compressible Euler and Navier-Stokes equations. This paper presents the TWS statement for the problem class range and highlights the important theoretical issues of accuracy, convergence and stability. Numerical results for a variety of benchmark problems are presented to document key features. 8 refs

  1. Further notes on convergence of the Weiszfeld algorithm

    Directory of Open Access Journals (Sweden)

    Brimberg Jack

    2003-01-01

    Full Text Available The Fermat-Weber problem is one of the most widely studied problems in classical location theory. In his previous work, Brimberg (1995 attempts to resolve a conjecture posed by Chandrasekaran and Tamir (1989 on a convergence property of the Weiszfeld algorithm, a well-known iterative procedure used to solve this problem. More recently, Canovas, Marin and Canavate (2002 provide counterexamples that appear to reopen the question. However, they do not attempt to reconcile their counterexamples with the previous work. We now show that in the light of these counterexamples, the proof is readily modified and the conjecture of Chandrasekaran and Tamir reclosed. .

  2. Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming

    NARCIS (Netherlands)

    Z-Q. Luo; J.F. Sturm; S. Zhang (Shuzhong)

    1996-01-01

    textabstractThis paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primal-dual optimal solution and that the size of the central path

  3. Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models

    International Nuclear Information System (INIS)

    Hsu, Cheng-Hsiung; Yang, Tzi-Sheng

    2013-01-01

    The purpose of this work is to investigate the existence, uniqueness, monotonicity and asymptotic behaviour of travelling wave solutions for a general epidemic model arising from the spread of an epidemic by oral–faecal transmission. First, we apply Schauder's fixed point theorem combining with a supersolution and subsolution pair to derive the existence of positive monotone monostable travelling wave solutions. Then, applying the Ikehara's theorem, we determine the exponential rates of travelling wave solutions which converge to two different equilibria as the moving coordinate tends to positive infinity and negative infinity, respectively. Finally, using the sliding method, we prove the uniqueness result provided the travelling wave solutions satisfy some boundedness conditions. (paper)

  4. A Constrained Algorithm Based NMFα for Image Representation

    Directory of Open Access Journals (Sweden)

    Chenxue Yang

    2014-01-01

    Full Text Available Nonnegative matrix factorization (NMF is a useful tool in learning a basic representation of image data. However, its performance and applicability in real scenarios are limited because of the lack of image information. In this paper, we propose a constrained matrix decomposition algorithm for image representation which contains parameters associated with the characteristics of image data sets. Particularly, we impose label information as additional hard constraints to the α-divergence-NMF unsupervised learning algorithm. The resulted algorithm is derived by using Karush-Kuhn-Tucker (KKT conditions as well as the projected gradient and its monotonic local convergence is proved by using auxiliary functions. In addition, we provide a method to select the parameters to our semisupervised matrix decomposition algorithm in the experiment. Compared with the state-of-the-art approaches, our method with the parameters has the best classification accuracy on three image data sets.

  5. Local Convergence and Radius of Convergence for Modified Newton Method

    Directory of Open Access Journals (Sweden)

    Măruşter Ştefan

    2017-12-01

    Full Text Available We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.

  6. Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

    Directory of Open Access Journals (Sweden)

    San-Yang Liu

    2014-01-01

    Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

  7. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

    Directory of Open Access Journals (Sweden)

    Xiangrong Li

    Full Text Available It is generally acknowledged that the conjugate gradient (CG method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

  8. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

    Science.gov (United States)

    Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

    2015-01-01

    It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

  9. Monotone Boolean functions

    International Nuclear Information System (INIS)

    Korshunov, A D

    2003-01-01

    Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years

  10. Convergence and resolution recovery of block-iterative EM algorithms modeling 3D detector response in SPECT

    International Nuclear Information System (INIS)

    Lalush, D.S.; Tsui, B.M.W.; Karimi, S.S.

    1996-01-01

    We evaluate fast reconstruction algorithms including ordered subsets-EM (OS-EM) and Rescaled Block Iterative EM (RBI-EM) in fully 3D SPECT applications on the basis of their convergence and resolution recovery properties as iterations proceed. Using a 3D computer-simulated phantom consisting of 3D Gaussian objects, we simulated projection data that includes only the effects of sampling and detector response of a parallel-hole collimator. Reconstructions were performed using each of the three algorithms (ML-EM, OS-EM, and RBI-EM) modeling the 3D detector response in the projection function. Resolution recovery was evaluated by fitting Gaussians to each of the four objects in the iterated image estimates at selected intervals. Results show that OS-EM and RBI-EM behave identically in this case; their resolution recovery results are virtually indistinguishable. Their resolution behavior appears to be very similar to that of ML-EM, but accelerated by a factor of twenty. For all three algorithms, smaller objects take more iterations to converge. Next, we consider the effect noise has on convergence. For both noise-free and noisy data, we evaluate the log likelihood function at each subiteration of OS-EM and RBI-EM, and at each iteration of ML-EM. With noisy data, both OS-EM and RBI-EM give results for which the log-likelihood function oscillates. Especially for 180-degree acquisitions, RBI-EM oscillates less than OS-EM. Both OS-EM and RBI-EM appear to converge to solutions, but not to the ML solution. We conclude that both OS-EM and RBI-EM can be effective algorithms for fully 3D SPECT reconstruction. Both recover resolution similarly to ML-EM, only more quickly

  11. Lacunary ideal convergence of multiple sequences

    Directory of Open Access Journals (Sweden)

    Bipan Hazarika

    2016-01-01

    Full Text Available An ideal I is a family of subsets of N×N which is closed under taking finite unions and subsets of its elements. In this article, the concept of lacunary ideal convergence of double sequences has been introduced. Also the relation between lacunary ideal convergent and lacunary Cauchy double sequences has been established. Furthermore, the notions of lacunary ideal limit point and lacunary ideal cluster points have been introduced and find the relation between these two notions. Finally, we have studied the properties such as solidity, monotonic.

  12. Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator

    KAUST Repository

    Bonito, Andrea

    2012-09-01

    We design and analyze variational and non-variational multigrid algorithms for the Laplace-Beltrami operator on a smooth and closed surface. In both cases, a uniform convergence for the V -cycle algorithm is obtained provided the surface geometry is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined directly on the smooth surface. In addition, the vanishing mean value constraint is imposed on each level, thereby avoiding singular quadratic forms without adding additional computational cost. Numerical results supporting our analysis are reported. In particular, the algorithms perform well even when applied to surfaces with a large aspect ratio. © 2011 American Mathematical Society.

  13. APPLICATION OF A PRIMAL-DUAL INTERIOR POINT ALGORITHM USING EXACT SECOND ORDER INFORMATION WITH A NOVEL NON-MONOTONE LINE SEARCH METHOD TO GENERALLY CONSTRAINED MINIMAX OPTIMISATION PROBLEMS

    Directory of Open Access Journals (Sweden)

    INTAN S. AHMAD

    2008-04-01

    Full Text Available This work presents the application of a primal-dual interior point method to minimax optimisation problems. The algorithm differs significantly from previous approaches as it involves a novel non-monotone line search procedure, which is based on the use of standard penalty methods as the merit function used for line search. The crucial novel concept is the discretisation of the penalty parameter used over a finite range of orders of magnitude and the provision of a memory list for each such order. An implementation within a logarithmic barrier algorithm for bounds handling is presented with capabilities for large scale application. Case studies presented demonstrate the capabilities of the proposed methodology, which relies on the reformulation of minimax models into standard nonlinear optimisation models. Some previously reported case studies from the open literature have been solved, and with significantly better optimal solutions identified. We believe that the nature of the non-monotone line search scheme allows the search procedure to escape from local minima, hence the encouraging results obtained.

  14. On convergence of differential evolution over a class of continuous functions with unique global optimum.

    Science.gov (United States)

    Ghosh, Sayan; Das, Swagatam; Vasilakos, Athanasios V; Suresh, Kaushik

    2012-02-01

    Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

  15. On utilization bounds for a periodic resource under rate monotonic scheduling

    NARCIS (Netherlands)

    Renssen, van A.M.; Geuns, S.J.; Hausmans, J.P.H.M.; Poncin, W.; Bril, R.J.

    2009-01-01

    This paper revisits utilization bounds for a periodic resource under the rate monotonic (RM) scheduling algorithm. We show that the existing utilization bound, as presented in [8, 9], is optimistic. We subsequently show that by viewing the unavailability of the periodic resource as a deferrable

  16. The Monotonic Lagrangian Grid for Rapid Air-Traffic Evaluation

    Science.gov (United States)

    Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay

    2010-01-01

    The Air Traffic Monotonic Lagrangian Grid (ATMLG) is presented as a tool to evaluate new air traffic system concepts. The model, based on an algorithm called the Monotonic Lagrangian Grid (MLG), can quickly sort, track, and update positions of many aircraft, both on the ground (at airports) and in the air. The underlying data structure is based on the MLG, which is used for sorting and ordering positions and other data needed to describe N moving bodies and their interactions. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. Recent upgrades to ATMLG include adding blank place-holders within the MLG data structure, which makes it possible to dynamically change the MLG size and also improves the quality of the MLG grid. Additional upgrades include adding FAA flight plan data, such as way-points and arrival and departure times from the Enhanced Traffic Management System (ETMS), and combining the MLG with the state-of-the-art strategic and tactical conflict detection and resolution algorithms from the NASA-developed Stratway software. In this paper, we present results from our early efforts to couple ATMLG with the Stratway software, and we demonstrate that it can be used to quickly simulate air traffic flow for a very large ETMS dataset.

  17. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    Higueras, Inmaculada

    2018-02-14

    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.

  18. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    Higueras, Inmaculada; Ketcheson, David I.; Kocsis, Tihamé r A.

    2018-01-01

    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.

  19. A PROOF OF CONVERGENCE OF THE HORN AND SCHUNCK OPTICAL FLOW ALGORITHM IN ARBITRARY DIMENSION

    Science.gov (United States)

    LE TARNEC, LOUIS; DESTREMPES, FRANÇOIS; CLOUTIER, GUY; GARCIA, DAMIEN

    2013-01-01

    The Horn and Schunck (HS) method, which amounts to the Jacobi iterative scheme in the interior of the image, was one of the first optical flow algorithms. In this article, we prove the convergence of the HS method, whenever the problem is well-posed. Our result is shown in the framework of a generalization of the HS method in dimension n ≥ 1, with a broad definition of the discrete Laplacian. In this context, the condition for the convergence is that the intensity gradients are not all contained in a same hyperplane. Two other articles ([17] and [13]) claimed to solve this problem in the case n = 2, but it appears that both of these proofs are erroneous. Moreover, we explain why some standard results on the convergence of the Jacobi method do not apply for the HS problem, unless n = 1. It is also shown that the convergence of the HS scheme implies the convergence of the Gauss-Seidel and SOR schemes for the HS problem. PMID:26097625

  20. Accelerated barrier optimization compressed sensing (ABOCS) for CT reconstruction with improved convergence

    International Nuclear Information System (INIS)

    Niu, Tianye; Fruhauf, Quentin; Petrongolo, Michael; Zhu, Lei; Ye, Xiaojing

    2014-01-01

    Recently, we proposed a new algorithm of accelerated barrier optimization compressed sensing (ABOCS) for iterative CT reconstruction. The previous implementation of ABOCS uses gradient projection (GP) with a Barzilai–Borwein (BB) step-size selection scheme (GP-BB) to search for the optimal solution. The algorithm does not converge stably due to its non-monotonic behavior. In this paper, we further improve the convergence of ABOCS using the unknown-parameter Nesterov (UPN) method and investigate the ABOCS reconstruction performance on clinical patient data. Comparison studies are carried out on reconstructions of computer simulation, a physical phantom and a head-and-neck patient. In all of these studies, the ABOCS results using UPN show more stable and faster convergence than those of the GP-BB method and a state-of-the-art Bregman-type method. As shown in the simulation study of the Shepp–Logan phantom, UPN achieves the same image quality as those of GP-BB and the Bregman-type methods, but reduces the iteration numbers by up to 50% and 90%, respectively. In the Catphan©600 phantom study, a high-quality image with relative reconstruction error (RRE) less than 3% compared to the full-view result is obtained using UPN with 17% projections (60 views). In the conventional filtered-backprojection reconstruction, the corresponding RRE is more than 15% on the same projection data. The superior performance of ABOCS with the UPN implementation is further demonstrated on the head-and-neck patient. Using 25% projections (91 views), the proposed method reduces the RRE from 21% as in the filtered backprojection (FBP) results to 7.3%. In conclusion, we propose UPN for ABOCS implementation. As compared to GP-BB and the Bregman-type methods, the new method significantly improves the convergence with higher stability and fewer iterations. (paper)

  1. Effects of Problem Decomposition (Partitioning) on the Rate of Convergence of Parallel Numerical Algorithms

    Czech Academy of Sciences Publication Activity Database

    Cullum, J. K.; Johnson, K.; Tůma, Miroslav

    2003-01-01

    Roč. 10, - (2003), s. 445-465 ISSN 1070-5325 R&D Projects: GA ČR GA201/02/0595; GA AV ČR IAA1030103 Institutional research plan: CEZ:AV0Z1030915 Keywords : parallel algorithms * graph partitioning * problem decomposition * rate of convergence Subject RIV: BA - General Mathematics Impact factor: 1.042, year: 2003

  2. Effect of inlect swirl on the convergence behavior of a combustor flow computation algorithm

    International Nuclear Information System (INIS)

    Shyy, W.; Braaten, M.E.; Hwang, T.H.

    1987-01-01

    The flow in a single sector of gas-turbine combustor with dilution holes has been studied numerically. It is found that there are some distinctive differences between the numerical behavior of the solution algorithm for combusting and noncombusting flows in a single-cup gas turbine combustor enclosed by four-sided solid walls. With the use of an iterative solution procedure and the standard κ-ε turbulence model, converged steady-state solutions are obtained for noncombusting flows with or without the presence of swirl of dilution jets. However, for the combusting flows, the interaction between the strength of the swirl ratio and the jet-to-main flow velocity ratio affects the ability of the algorithm to achieve a converged steady-state solution. Increasing inlet swirl causes the flow field to oscillate as the iterations progress, and to fail to reach a steady-state solution, while increasing the flow through the dilution jets helps achieve a steady-state solution. The above phenomena are not observed for the flows with periodic boundary conditions along two side planes

  3. Monotonic Set-Extended Prefix Rewriting and Verification of Recursive Ping-Pong Protocols

    DEFF Research Database (Denmark)

    Delzanno, Giorgio; Esparza, Javier; Srba, Jiri

    2006-01-01

    of messages) some verification problems become decidable. In particular we give an algorithm to decide control state reachability, a problem related to security properties like secrecy and authenticity. The proof is via a reduction to a new prefix rewriting model called Monotonic Set-extended Prefix rewriting...

  4. Convergence theorems for certain classes of nonlinear mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1992-01-01

    Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs

  5. Matching by Monotonic Tone Mapping.

    Science.gov (United States)

    Kovacs, Gyorgy

    2018-06-01

    In this paper, a novel dissimilarity measure called Matching by Monotonic Tone Mapping (MMTM) is proposed. The MMTM technique allows matching under non-linear monotonic tone mappings and can be computed efficiently when the tone mappings are approximated by piecewise constant or piecewise linear functions. The proposed method is evaluated in various template matching scenarios involving simulated and real images, and compared to other measures developed to be invariant to monotonic intensity transformations. The results show that the MMTM technique is a highly competitive alternative of conventional measures in problems where possible tone mappings are close to monotonic.

  6. BIMOND3, Monotone Bivariate Interpolation

    International Nuclear Information System (INIS)

    Fritsch, F.N.; Carlson, R.E.

    2001-01-01

    1 - Description of program or function: BIMOND is a FORTRAN-77 subroutine for piecewise bi-cubic interpolation to data on a rectangular mesh, which reproduces the monotonousness of the data. A driver program, BIMOND1, is provided which reads data, computes the interpolating surface parameters, and evaluates the function on a mesh suitable for plotting. 2 - Method of solution: Monotonic piecewise bi-cubic Hermite interpolation is used. 3 - Restrictions on the complexity of the problem: The current version of the program can treat data which are monotone in only one of the independent variables, but cannot handle piecewise monotone data

  7. A Nonmonotone Line Search Filter Algorithm for the System of Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Zhong Jin

    2012-01-01

    Full Text Available We present a new iterative method based on the line search filter method with the nonmonotone strategy to solve the system of nonlinear equations. The equations are divided into two groups; some equations are treated as constraints and the others act as the objective function, and the two groups are just updated at the iterations where it is needed indeed. We employ the nonmonotone idea to the sufficient reduction conditions and filter technique which leads to a flexibility and acceptance behavior comparable to monotone methods. The new algorithm is shown to be globally convergent and numerical experiments demonstrate its effectiveness.

  8. Convergence criteria for systems of nonlinear elliptic partial differential equations

    International Nuclear Information System (INIS)

    Sharma, R.K.

    1986-01-01

    This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

  9. Generalized monotone operators in Banach spaces

    International Nuclear Information System (INIS)

    Nanda, S.

    1988-07-01

    The concept of F-monotonicity was first introduced by Kato and this generalizes the notion of monotonicity introduced by Minty. The purpose of this paper is to define various types of F-monotonicities and discuss the relationships among them. (author). 6 refs

  10. Convergence of Hybrid Space Mapping Algorithms

    DEFF Research Database (Denmark)

    Madsen, Kaj; Søndergaard, Jacob

    2004-01-01

    may be poor, or the method may even fail to converge to a stationary point. We consider a convex combination of the space mapping technique with a classical optimization technique. The function to be optimized has the form \\$H \\$\\backslash\\$circ f\\$ where \\$H: \\$\\backslash\\$dR\\^m \\$\\backslash......\\$mapsto \\$\\backslash\\$dR\\$ is convex and \\$f: \\$\\backslash\\$dR\\^n \\$\\backslash\\$mapsto \\$\\backslash\\$dR\\^m\\$ is smooth. Experience indicates that the combined method maintains the initial efficiency of the space mapping technique. We prove that the global convergence property of the classical technique is also...

  11. A Design Algorithm using External Perturbation to Improve Iterative Feedback Tuning Convergence

    DEFF Research Database (Denmark)

    Huusom, Jakob Kjøbsted; Hjalmarsson, Håkan; Poulsen, Niels Kjølstad

    2011-01-01

    Iterative Feedback Tuning constitutes an attractive control loop tuning method for processes in the absence of process insight. It is a purely data driven approach for optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost function...... gradient, which is used in a search algorithm for minimizing the performance cost. A slow rate of convergence of the tuning method is often experienced when tuning for disturbance rejection. This is due to a poor signal to noise ratio in the process data. A method is proposed for increasing the data...

  12. Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models.

    Science.gov (United States)

    Chen, Baojiang; Qin, Jing

    2014-05-10

    In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study. Copyright © 2013 John Wiley & Sons, Ltd.

  13. Optimal Monotone Drawings of Trees

    OpenAIRE

    He, Dayu; He, Xin

    2016-01-01

    A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists abpath P_{uw} in G that is monotone in some direction l_{uw}. (Namely, the order of the orthogonal projections of the vertices of P_{uw} on l_{uw} is the same as the order they appear in P_{uw}.) The problem of finding monotone drawings for trees has been studied in several recent papers. The main focus is to reduce the size of the drawing. Currently, the smallest drawi...

  14. Multipartite classical and quantum secrecy monotones

    International Nuclear Information System (INIS)

    Cerf, N.J.; Massar, S.; Schneider, S.

    2002-01-01

    In order to study multipartite quantum cryptography, we introduce quantities which vanish on product probability distributions, and which can only decrease if the parties carry out local operations or public classical communication. These 'secrecy monotones' therefore measure how much secret correlation is shared by the parties. In the bipartite case we show that the mutual information is a secrecy monotone. In the multipartite case we describe two different generalizations of the mutual information, both of which are secrecy monotones. The existence of two distinct secrecy monotones allows us to show that in multipartite quantum cryptography the parties must make irreversible choices about which multipartite correlations they want to obtain. Secrecy monotones can be extended to the quantum domain and are then defined on density matrices. We illustrate this generalization by considering tripartite quantum cryptography based on the Greenberger-Horne-Zeilinger state. We show that before carrying out measurements on the state, the parties must make an irreversible decision about what probability distribution they want to obtain

  15. Surface meshing with curvature convergence

    KAUST Repository

    Li, Huibin; Zeng, Wei; Morvan, Jean-Marie; Chen, Liming; Gu, Xianfengdavid

    2014-01-01

    Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.

  16. Surface meshing with curvature convergence

    KAUST Repository

    Li, Huibin

    2014-06-01

    Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.

  17. Analysis of Different Feature Selection Criteria Based on a Covariance Convergence Perspective for a SLAM Algorithm

    Science.gov (United States)

    Auat Cheein, Fernando A.; Carelli, Ricardo

    2011-01-01

    This paper introduces several non-arbitrary feature selection techniques for a Simultaneous Localization and Mapping (SLAM) algorithm. The feature selection criteria are based on the determination of the most significant features from a SLAM convergence perspective. The SLAM algorithm implemented in this work is a sequential EKF (Extended Kalman filter) SLAM. The feature selection criteria are applied on the correction stage of the SLAM algorithm, restricting it to correct the SLAM algorithm with the most significant features. This restriction also causes a decrement in the processing time of the SLAM. Several experiments with a mobile robot are shown in this work. The experiments concern the map reconstruction and a comparison between the different proposed techniques performance. The experiments were carried out at an outdoor environment composed by trees, although the results shown herein are not restricted to a special type of features. PMID:22346568

  18. Modeling non-monotonic properties under propositional argumentation

    Science.gov (United States)

    Wang, Geng; Lin, Zuoquan

    2013-03-01

    In the field of knowledge representation, argumentation is usually considered as an abstract framework for nonclassical logic. In this paper, however, we'd like to present a propositional argumentation framework, which can be used to closer simulate a real-world argumentation. We thereby argue that under a dialectical argumentation game, we can allow non-monotonic reasoning even under classical logic. We introduce two methods together for gaining nonmonotonicity, one by giving plausibility for arguments, the other by adding "exceptions" which is similar to defaults. Furthermore, we will give out an alternative definition for propositional argumentation using argumentative models, which is highly related to the previous reasoning method, but with a simple algorithm for calculation.

  19. Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem

    International Nuclear Information System (INIS)

    Klibanov, Michael V; Pantong, Natee; Fiddy, Michael A; Schenk, John; Beilina, Larisa

    2010-01-01

    A globally convergent algorithm by the first and third authors for a 3D hyperbolic coefficient inverse problem is verified on experimental data measured in the picosecond scale regime. Quantifiable images of dielectric abnormalities are obtained. The total measurement timing of a 100 ps pulse for one detector location was 1.2 ns with 20 ps (=0.02 ns) time step between two consecutive readings. Blind tests have consistently demonstrated an accurate imaging of refractive indexes of dielectric abnormalities. At the same time, it is shown that a modified gradient method is inapplicable to this kind of experimental data. This inverse algorithm is also applicable to other types of imaging modalities, e.g. acoustics. Potential applications are in airport security, imaging of land mines, imaging of defects in non-distractive testing, etc

  20. Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays

    International Nuclear Information System (INIS)

    Liao Xiaofeng; Wong, K.-W.; Yang Shizhong

    2003-01-01

    In this Letter, the characteristics of the convergence dynamics of hybrid bidirectional associative memory neural networks with distributed transmission delays are studied. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the Lyapunov functionals are constructed and the generalized Halanay-type inequalities are employed to derive the delay-independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs. Some examples are given to illustrate the correctness of our results

  1. Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

    Science.gov (United States)

    Wei, Qinglai; Liu, Derong; Lin, Hanquan

    2016-03-01

    In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

  2. Convergent Difference Schemes for Hamilton-Jacobi equations

    KAUST Repository

    Duisembay, Serikbolsyn

    2018-05-07

    In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet and Neumann type boundary conditions in arbitrary two-dimensional domains. First, we introduce the notion of viscosity solutions in both continuous and discontinuous frameworks. Next, we review Barles-Souganidis approach using monotone, consistent, and stable schemes. In particular, we show that these schemes converge locally uniformly to the unique viscosity solution of the first-order Hamilton-Jacobi equations under mild assumptions. To solve the scheme numerically, we use Euler map with some initial guess. This iterative method gives the viscosity solution as a limit. Moreover, we illustrate our numerical approach in several two-dimensional examples.

  3. Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

    Science.gov (United States)

    Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

    2017-12-01

    This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

  4. The Monotonicity Puzzle: An Experimental Investigation of Incentive Structures

    Directory of Open Access Journals (Sweden)

    Jeannette Brosig

    2010-05-01

    Full Text Available Non-monotone incentive structures, which - according to theory - are able to induce optimal behavior, are often regarded as empirically less relevant for labor relationships. We compare the performance of a theoretically optimal non-monotone contract with a monotone one under controlled laboratory conditions. Implementing some features relevant to real-world employment relationships, our paper demonstrates that, in fact, the frequency of income-maximizing decisions made by agents is higher under the monotone contract. Although this observed behavior does not change the superiority of the non-monotone contract for principals, they do not choose this contract type in a significant way. This is what we call the monotonicity puzzle. Detailed investigations of decisions provide a clue for solving the puzzle and a possible explanation for the popularity of monotone contracts.

  5. An Ensemble Approach in Converging Contents of LMS and KMS

    Science.gov (United States)

    Sabitha, A. Sai; Mehrotra, Deepti; Bansal, Abhay

    2017-01-01

    Currently the challenges in e-Learning are converging the learning content from various sources and managing them within e-learning practices. Data mining learning algorithms can be used and the contents can be converged based on the Metadata of the objects. Ensemble methods use multiple learning algorithms and it can be used to converge the…

  6. Study of the convergence behavior of the complex kernel least mean square algorithm.

    Science.gov (United States)

    Paul, Thomas K; Ogunfunmi, Tokunbo

    2013-09-01

    The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

  7. Reliability enhancement of Navier-Stokes codes through convergence acceleration

    Science.gov (United States)

    Merkle, Charles L.; Dulikravich, George S.

    1995-01-01

    Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

  8. On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity

    KAUST Repository

    Pettersson, Per

    2013-05-01

    The stochastic Galerkin and collocation methods are used to solve an advection-diffusion equation with uncertain and spatially varying viscosity. We investigate well-posedness, monotonicity and stability for the extended system resulting from the Galerkin projection of the advection-diffusion equation onto the stochastic basis functions. High-order summation-by-parts operators and weak imposition of boundary conditions are used to prove stability of the semi-discrete system.It is essential that the eigenvalues of the resulting viscosity matrix of the stochastic Galerkin system are positive and we investigate conditions for this to hold. When the viscosity matrix is diagonalizable, stochastic Galerkin and stochastic collocation are similar in terms of computational cost, and for some cases the accuracy is higher for stochastic Galerkin provided that monotonicity requirements are met. We also investigate the total spatial operator of the semi-discretized system and its impact on the convergence to steady-state. © 2013 Elsevier B.V.

  9. On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity

    KAUST Repository

    Pettersson, Per; Doostan, Alireza; Nordströ m, Jan

    2013-01-01

    The stochastic Galerkin and collocation methods are used to solve an advection-diffusion equation with uncertain and spatially varying viscosity. We investigate well-posedness, monotonicity and stability for the extended system resulting from the Galerkin projection of the advection-diffusion equation onto the stochastic basis functions. High-order summation-by-parts operators and weak imposition of boundary conditions are used to prove stability of the semi-discrete system.It is essential that the eigenvalues of the resulting viscosity matrix of the stochastic Galerkin system are positive and we investigate conditions for this to hold. When the viscosity matrix is diagonalizable, stochastic Galerkin and stochastic collocation are similar in terms of computational cost, and for some cases the accuracy is higher for stochastic Galerkin provided that monotonicity requirements are met. We also investigate the total spatial operator of the semi-discretized system and its impact on the convergence to steady-state. © 2013 Elsevier B.V.

  10. Convergence of finite differences schemes for viscous and inviscid conservation laws with rough coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

    2000-09-01

    We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a ''rough'' coefficient function k(x). we show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. (author)

  11. Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

    International Nuclear Information System (INIS)

    Wan Li; Zhou Qinghua

    2007-01-01

    The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem

  12. Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

    Science.gov (United States)

    Wan, Li; Zhou, Qinghua

    2007-10-01

    The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

  13. Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

    Science.gov (United States)

    Tijmstra, Jesper; Hessen, David J.; van der Heijden, Peter G. M.; Sijtsma, Klaas

    2013-01-01

    Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores,…

  14. Simultaneous solution algorithms for Eulerian-Eulerian gas-solid flow models: Stability analysis and convergence behaviour of a point and a plane solver

    International Nuclear Information System (INIS)

    Wilde, Juray de; Vierendeels, Jan; Heynderickx, Geraldine J.; Marin, Guy B.

    2005-01-01

    Simultaneous solution algorithms for Eulerian-Eulerian gas-solid flow models are presented and their stability analyzed. The integration algorithms are based on dual-time stepping with fourth-order Runge-Kutta in pseudo-time. The domain is solved point or plane wise. The discretization of the inviscid terms is based on a low-Mach limit of the multi-phase preconditioned advection upstream splitting method (MP-AUSMP). The numerical stability of the simultaneous solution algorithms is analyzed in 2D with the Fourier method. Stability results are compared with the convergence behaviour of 3D riser simulations. The impact of the grid aspect ratio, preconditioning, artificial dissipation, and the treatment of the source terms is investigated. A particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the Eulerian-Eulerian gas-solid flow models and their solution. The numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas-solid slip velocities. Furthermore, the effect of the grid resolution on the convergence behaviour and the simulation results is investigated. Finally, simulations of the bottom zone of a pilot-scale riser with a side solids inlet are experimentally validated

  15. Strong monotonicity in mixed-state entanglement manipulation

    International Nuclear Information System (INIS)

    Ishizaka, Satoshi

    2006-01-01

    A strong entanglement monotone, which never increases under local operations and classical communications (LOCC), restricts quantum entanglement manipulation more strongly than the usual monotone since the usual one does not increase on average under LOCC. We propose strong monotones in mixed-state entanglement manipulation under LOCC. These are related to the decomposability and one-positivity of an operator constructed from a quantum state, and reveal geometrical characteristics of entangled states. These are lower bounded by the negativity or generalized robustness of entanglement

  16. Transmission-less attenuation correction in time-of-flight PET: analysis of a discrete iterative algorithm

    International Nuclear Information System (INIS)

    Defrise, Michel; Rezaei, Ahmadreza; Nuyts, Johan

    2014-01-01

    The maximum likelihood attenuation correction factors (MLACF) algorithm has been developed to calculate the maximum-likelihood estimate of the activity image and the attenuation sinogram in time-of-flight (TOF) positron emission tomography, using only emission data without prior information on the attenuation. We consider the case of a Poisson model of the data, in the absence of scatter or random background. In this case the maximization with respect to the attenuation factors can be achieved in a closed form and the MLACF algorithm works by updating the activity. Despite promising numerical results, the convergence of this algorithm has not been analysed. In this paper we derive the algorithm and demonstrate that the MLACF algorithm monotonically increases the likelihood, is asymptotically regular, and that the limit points of the iteration are stationary points of the likelihood. Because the problem is not convex, however, the limit points might be saddle points or local maxima. To obtain some empirical insight into the latter question, we present data obtained by applying MLACF to 2D simulated TOF data, using a large number of iterations and different initializations. (paper)

  17. A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Wiyada Kumam

    2016-05-01

    Full Text Available In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field.

  18. Generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone operators with applications in non-compact settings and minimization problems

    Directory of Open Access Journals (Sweden)

    Chowdhury Molhammad SR

    2000-01-01

    Full Text Available Results are obtained on existence theorems of generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone operators in both compact and non-compact settings. We shall use the concept of escaping sequences introduced by Border (Fixed Point Theorem with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, 1985 to obtain results in non-compact settings. Existence theorems on non-compact generalized bi-complementarity problems for quasi-semi-monotone and bi-quasi-semi-monotone operators are also obtained. Moreover, as applications of some results of this paper on generalized bi-quasi-variational inequalities, we shall obtain existence of solutions for some kind of minimization problems with quasi- semi-monotone and bi-quasi-semi-monotone operators.

  19. Properties of a genetic algorithm extended by a random self-learning operator and asymmetric mutations: A convergence study for a task of powder-pattern indexing

    International Nuclear Information System (INIS)

    Paszkowicz, Wojciech

    2006-01-01

    Genetic algorithms represent a powerful global-optimisation tool applicable in solving tasks of high complexity in science, technology, medicine, communication, etc. The usual genetic-algorithm calculation scheme is extended here by introduction of a quadratic self-learning operator, which performs a partial local search for randomly selected representatives of the population. This operator is aimed as a minor deterministic contribution to the (stochastic) genetic search. The population representing the trial solutions is split into two equal subpopulations allowed to exhibit different mutation rates (so called asymmetric mutation). The convergence is studied in detail exploiting a crystallographic-test example of indexing of powder diffraction data of orthorhombic lithium copper oxide, varying such parameters as mutation rates and the learning rate. It is shown through the averaged (over the subpopulation) fitness behaviour, how the genetic diversity in the population depends on the mutation rate of the given subpopulation. Conditions and algorithm parameter values favourable for convergence in the framework of proposed approach are discussed using the results for the mentioned example. Further data are studied with a somewhat modified algorithm using periodically varying mutation rates and a problem-specific operator. The chance of finding the global optimum and the convergence speed are observed to be strongly influenced by the effective mutation level and on the self-learning level. The optimal values of these two parameters are about 6 and 5%, respectively. The periodic changes of mutation rate are found to improve the explorative abilities of the algorithm. The results of the study confirm that the applied methodology leads to improvement of the classical genetic algorithm and, therefore, it is expected to be helpful in constructing of algorithms permitting to solve similar tasks of higher complexity

  20. Hybrid Algorithm of Particle Swarm Optimization and Grey Wolf Optimizer for Improving Convergence Performance

    Directory of Open Access Journals (Sweden)

    Narinder Singh

    2017-01-01

    Full Text Available A newly hybrid nature inspired algorithm called HPSOGWO is presented with the combination of Particle Swarm Optimization (PSO and Grey Wolf Optimizer (GWO. The main idea is to improve the ability of exploitation in Particle Swarm Optimization with the ability of exploration in Grey Wolf Optimizer to produce both variants’ strength. Some unimodal, multimodal, and fixed-dimension multimodal test functions are used to check the solution quality and performance of HPSOGWO variant. The numerical and statistical solutions show that the hybrid variant outperforms significantly the PSO and GWO variants in terms of solution quality, solution stability, convergence speed, and ability to find the global optimum.

  1. Specific non-monotonous interactions increase persistence of ecological networks.

    Science.gov (United States)

    Yan, Chuan; Zhang, Zhibin

    2014-03-22

    The relationship between stability and biodiversity has long been debated in ecology due to opposing empirical observations and theoretical predictions. Species interaction strength is often assumed to be monotonically related to population density, but the effects on stability of ecological networks of non-monotonous interactions that change signs have not been investigated previously. We demonstrate that for four kinds of non-monotonous interactions, shifting signs to negative or neutral interactions at high population density increases persistence (a measure of stability) of ecological networks, while for the other two kinds of non-monotonous interactions shifting signs to positive interactions at high population density decreases persistence of networks. Our results reveal a novel mechanism of network stabilization caused by specific non-monotonous interaction types through either increasing stable equilibrium points or reducing unstable equilibrium points (or both). These specific non-monotonous interactions may be important in maintaining stable and complex ecological networks, as well as other networks such as genes, neurons, the internet and human societies.

  2. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter; Taká č, Martin

    2017-01-01

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  3. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter

    2017-06-04

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  4. On the size of monotone span programs

    NARCIS (Netherlands)

    Nikov, V.S.; Nikova, S.I.; Preneel, B.; Blundo, C.; Cimato, S.

    2005-01-01

    Span programs provide a linear algebraic model of computation. Monotone span programs (MSP) correspond to linear secret sharing schemes. This paper studies the properties of monotone span programs related to their size. Using the results of van Dijk (connecting codes and MSPs) and a construction for

  5. Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

    KAUST Repository

    Hundsdorfer, W.

    2011-04-29

    In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.

  6. Convergence analysis for column-action methods in image reconstruction

    DEFF Research Database (Denmark)

    Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj

    2016-01-01

    Column-oriented versions of algebraic iterative methods are interesting alternatives to their row-version counterparts: they converge to a least squares solution, and they provide a basis for saving computational work by skipping small updates. In this paper we consider the case of noise-free data....... We present a convergence analysis of the column algorithms, we discuss two techniques (loping and flagging) for reducing the work, and we establish some convergence results for methods that utilize these techniques. The performance of the algorithms is illustrated with numerical examples from...

  7. Type monotonic allocation schemes for multi-glove games

    OpenAIRE

    Brânzei, R.; Solymosi, T.; Tijs, S.H.

    2007-01-01

    Multiglove markets and corresponding games are considered.For this class of games we introduce the notion of type monotonic allocation scheme.Allocation rules for multiglove markets based on weight systems are introduced and characterized.These allocation rules generate type monotonic allocation schemes for multiglove games and are also helpful in proving that each core element of the corresponding game is extendable to a type monotonic allocation scheme.The T-value turns out to generate a ty...

  8. Moduli and Characteristics of Monotonicity in Some Banach Lattices

    Directory of Open Access Journals (Sweden)

    Miroslav Krbec

    2010-01-01

    Full Text Available First the characteristic of monotonicity of any Banach lattice X is expressed in terms of the left limit of the modulus of monotonicity of X at the point 1. It is also shown that for Köthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity δ^m,E. The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008 which establish that Banach lattices X with ε0,m(X<1 and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001.

  9. Edit Distance to Monotonicity in Sliding Windows

    DEFF Research Database (Denmark)

    Chan, Ho-Leung; Lam, Tak-Wah; Lee, Lap Kei

    2011-01-01

    Given a stream of items each associated with a numerical value, its edit distance to monotonicity is the minimum number of items to remove so that the remaining items are non-decreasing with respect to the numerical value. The space complexity of estimating the edit distance to monotonicity of a ...

  10. System convergence in transport models: algorithms efficiency and output uncertainty

    DEFF Research Database (Denmark)

    Rich, Jeppe; Nielsen, Otto Anker

    2015-01-01

    of this paper is to analyse convergence performance for the external loop and to illustrate how an improper linkage between the converging parts can lead to substantial uncertainty in the final output. Although this loop is crucial for the performance of large-scale transport models it has not been analysed...... much in the literature. The paper first investigates several variants of the Method of Successive Averages (MSA) by simulation experiments on a toy-network. It is found that the simulation experiments produce support for a weighted MSA approach. The weighted MSA approach is then analysed on large......-scale in the Danish National Transport Model (DNTM). It is revealed that system convergence requires that either demand or supply is without random noise but not both. In that case, if MSA is applied to the model output with random noise, it will converge effectively as the random effects are gradually dampened...

  11. The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation

    Science.gov (United States)

    Alexandrov, Natalia; Kaplan, Carolyn; Oran, Elaine; Boris, Jay

    2010-01-01

    This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.

  12. A non-parametric test for partial monotonicity in multiple regression

    NARCIS (Netherlands)

    van Beek, M.; Daniëls, H.A.M.

    Partial positive (negative) monotonicity in a dataset is the property that an increase in an independent variable, ceteris paribus, generates an increase (decrease) in the dependent variable. A test for partial monotonicity in datasets could (1) increase model performance if monotonicity may be

  13. Log-binomial models: exploring failed convergence.

    Science.gov (United States)

    Williamson, Tyler; Eliasziw, Misha; Fick, Gordon Hilton

    2013-12-13

    Relative risk is a summary metric that is commonly used in epidemiological investigations. Increasingly, epidemiologists are using log-binomial models to study the impact of a set of predictor variables on a single binary outcome, as they naturally offer relative risks. However, standard statistical software may report failed convergence when attempting to fit log-binomial models in certain settings. The methods that have been proposed in the literature for dealing with failed convergence use approximate solutions to avoid the issue. This research looks directly at the log-likelihood function for the simplest log-binomial model where failed convergence has been observed, a model with a single linear predictor with three levels. The possible causes of failed convergence are explored and potential solutions are presented for some cases. Among the principal causes is a failure of the fitting algorithm to converge despite the log-likelihood function having a single finite maximum. Despite these limitations, log-binomial models are a viable option for epidemiologists wishing to describe the relationship between a set of predictors and a binary outcome where relative risk is the desired summary measure. Epidemiologists are encouraged to continue to use log-binomial models and advocate for improvements to the fitting algorithms to promote the widespread use of log-binomial models.

  14. Foundations of genetic algorithms 1991

    CERN Document Server

    1991-01-01

    Foundations of Genetic Algorithms 1991 (FOGA 1) discusses the theoretical foundations of genetic algorithms (GA) and classifier systems.This book compiles research papers on selection and convergence, coding and representation, problem hardness, deception, classifier system design, variation and recombination, parallelization, and population divergence. Other topics include the non-uniform Walsh-schema transform; spurious correlations and premature convergence in genetic algorithms; and variable default hierarchy separation in a classifier system. The grammar-based genetic algorithm; condition

  15. A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints

    International Nuclear Information System (INIS)

    Chen, Z.-W.; Han, J.-Y.; Xu, D.-C.

    2001-01-01

    In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient

  16. Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm. (On-Line Harmonics Estimation Application

    Directory of Open Access Journals (Sweden)

    Eyad K Almaita

    2017-03-01

    Keywords: Energy efficiency, Power quality, Radial basis function, neural networks, adaptive, harmonic. Article History: Received Dec 15, 2016; Received in revised form Feb 2nd 2017; Accepted 13rd 2017; Available online How to Cite This Article: Almaita, E.K and Shawawreh J.Al (2017 Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm (On-Line Harmonics Estimation Application.  International Journal of Renewable Energy Develeopment, 6(1, 9-17. http://dx.doi.org/10.14710/ijred.6.1.9-17

  17. Testing manifest monotonicity using order-constrained statistical inference

    NARCIS (Netherlands)

    Tijmstra, J.; Hessen, D.J.; van der Heijden, P.G.M.; Sijtsma, K.

    2013-01-01

    Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest

  18. Monotonicity-based electrical impedance tomography for lung imaging

    Science.gov (United States)

    Zhou, Liangdong; Harrach, Bastian; Seo, Jin Keun

    2018-04-01

    This paper presents a monotonicity-based spatiotemporal conductivity imaging method for continuous regional lung monitoring using electrical impedance tomography (EIT). The EIT data (i.e. the boundary current-voltage data) can be decomposed into pulmonary, cardiac and other parts using their different periodic natures. The time-differential current-voltage operator corresponding to the lung ventilation can be viewed as either semi-positive or semi-negative definite owing to monotonic conductivity changes within the lung regions. We used these monotonicity constraints to improve the quality of lung EIT imaging. We tested the proposed methods in numerical simulations, phantom experiments and human experiments.

  19. Existence and convergence theorems for evolutionary hemivariational inequalities of second order

    Directory of Open Access Journals (Sweden)

    Zijia Peng

    2015-03-01

    Full Text Available This article concerns with a class of evolutionary hemivariational inequalities in the framework of evolution triple. Based on the Rothe method, monotonicity-compactness technique and the properties of Clarke's generalized derivative and gradient, the existence and convergence theorems to these problems are established. The main idea in the proof is using the time difference to construct the approximate problems. The work generalizes the existence results on evolution inclusions and hemivariational inequalities of second order.

  20. On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

    International Nuclear Information System (INIS)

    Xu, Meng; Droguett, Enrique López; Lins, Isis Didier; Chagas Moura, Márcio das

    2017-01-01

    The q-Weibull model is based on the Tsallis non-extensive entropy and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the q-Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate. - Highlights: • Development of an Adaptive Hybrid ABC (AHABC) algorithm for q-Weibull distribution. • AHABC combines local Nelder-Mead simplex method with ABC to enhance local search. • AHABC efficiently finds the optimal solution for the q-Weibull ML problem. • AHABC outperforms ABC and self-adaptive hybrid ABC in accuracy and convergence speed. • Useful model for reliability data with non-monotonic hazard rate.

  1. Monotonicity of fitness landscapes and mutation rate control.

    Science.gov (United States)

    Belavkin, Roman V; Channon, Alastair; Aston, Elizabeth; Aston, John; Krašovec, Rok; Knight, Christopher G

    2016-12-01

    A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.

  2. Fast convergent frequency-domain MIMO equalizer for few-mode fiber communication systems

    Science.gov (United States)

    He, Xuan; Weng, Yi; Wang, Junyi; Pan, Z.

    2018-02-01

    Space division multiplexing using few-mode fibers has been extensively explored to sustain the continuous traffic growth. In few-mode fiber optical systems, both spatial and polarization modes are exploited to transmit parallel channels, thus increasing the overall capacity. However, signals on spatial channels inevitably suffer from the intrinsic inter-modal coupling and large accumulated differential mode group delay (DMGD), which causes spatial modes de-multiplex even harder. Many research articles have demonstrated that frequency domain adaptive multi-input multi-output (MIMO) equalizer can effectively compensate the DMGD and demultiplex the spatial channels with digital signal processing (DSP). However, the large accumulated DMGD usually requires a large number of training blocks for the initial convergence of adaptive MIMO equalizers, which will decrease the overall system efficiency and even degrade the equalizer performance in fast-changing optical channels. Least mean square (LMS) algorithm is always used in MIMO equalization to dynamically demultiplex the spatial signals. We have proposed to use signal power spectral density (PSD) dependent method and noise PSD directed method to improve the convergence speed of adaptive frequency domain LMS algorithm. We also proposed frequency domain recursive least square (RLS) algorithm to further increase the convergence speed of MIMO equalizer at cost of greater hardware complexity. In this paper, we will compare the hardware complexity and convergence speed of signal PSD dependent and noise power directed algorithms against the conventional frequency domain LMS algorithm. In our numerical study of a three-mode 112 Gbit/s PDM-QPSK optical system with 3000 km transmission, the noise PSD directed and signal PSD dependent methods could improve the convergence speed by 48.3% and 36.1% respectively, at cost of 17.2% and 10.7% higher hardware complexity. We will also compare the frequency domain RLS algorithm against

  3. Eigenvalue Decomposition-Based Modified Newton Algorithm

    Directory of Open Access Journals (Sweden)

    Wen-jun Wang

    2013-01-01

    Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.

  4. A Multistrategy Optimization Improved Artificial Bee Colony Algorithm

    Directory of Open Access Journals (Sweden)

    Wen Liu

    2014-01-01

    Full Text Available Being prone to the shortcomings of premature and slow convergence rate of artificial bee colony algorithm, an improved algorithm was proposed. Chaotic reverse learning strategies were used to initialize swarm in order to improve the global search ability of the algorithm and keep the diversity of the algorithm; the similarity degree of individuals of the population was used to characterize the diversity of population; population diversity measure was set as an indicator to dynamically and adaptively adjust the nectar position; the premature and local convergence were avoided effectively; dual population search mechanism was introduced to the search stage of algorithm; the parallel search of dual population considerably improved the convergence rate. Through simulation experiments of 10 standard testing functions and compared with other algorithms, the results showed that the improved algorithm had faster convergence rate and the capacity of jumping out of local optimum faster.

  5. On the premature convergence of particle swarm optimization

    DEFF Research Database (Denmark)

    Larsen, Rie B.; Jouffroy, Jerome; Lassen, Benny

    2016-01-01

    This paper discusses convergence issues of the basic particle swarm optimization algorithm for different pa- rameters. For the one-dimensional case, it is shown that, for a specific range of parameters, the particles will converge prematurely, i.e. away from the actual minimum of the objective...

  6. Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

    KAUST Repository

    Hundsdorfer, W.; Mozartova, A.; Spijker, M. N.

    2011-01-01

    In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many

  7. Modified Clipped LMS Algorithm

    Directory of Open Access Journals (Sweden)

    Lotfizad Mojtaba

    2005-01-01

    Full Text Available Abstract A new algorithm is proposed for updating the weights of an adaptive filter. The proposed algorithm is a modification of an existing method, namely, the clipped LMS, and uses a three-level quantization ( scheme that involves the threshold clipping of the input signals in the filter weight update formula. Mathematical analysis shows the convergence of the filter weights to the optimum Wiener filter weights. Also, it can be proved that the proposed modified clipped LMS (MCLMS algorithm has better tracking than the LMS algorithm. In addition, this algorithm has reduced computational complexity relative to the unmodified one. By using a suitable threshold, it is possible to increase the tracking capability of the MCLMS algorithm compared to the LMS algorithm, but this causes slower convergence. Computer simulations confirm the mathematical analysis presented.

  8. Convolutional Dictionary Learning: Acceleration and Convergence

    Science.gov (United States)

    Chun, Il Yong; Fessler, Jeffrey A.

    2018-04-01

    Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared to the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large datasets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.

  9. Assessing the Health of LiFePO4 Traction Batteries through Monotonic Echo State Networks

    Science.gov (United States)

    Anseán, David; Otero, José; Couso, Inés

    2017-01-01

    A soft sensor is presented that approximates certain health parameters of automotive rechargeable batteries from on-vehicle measurements of current and voltage. The sensor is based on a model of the open circuit voltage curve. This last model is implemented through monotonic neural networks and estimate over-potentials arising from the evolution in time of the Lithium concentration in the electrodes of the battery. The proposed soft sensor is able to exploit the information contained in operational records of the vehicle better than the alternatives, this being particularly true when the charge or discharge currents are between moderate and high. The accuracy of the neural model has been compared to different alternatives, including data-driven statistical models, first principle-based models, fuzzy observers and other recurrent neural networks with different topologies. It is concluded that monotonic echo state networks can outperform well established first-principle models. The algorithms have been validated with automotive Li-FePO4 cells. PMID:29267219

  10. Assessing the Health of LiFePO4 Traction Batteries through Monotonic Echo State Networks

    Directory of Open Access Journals (Sweden)

    Luciano Sánchez

    2017-12-01

    Full Text Available A soft sensor is presented that approximates certain health parameters of automotive rechargeable batteries from on-vehicle measurements of current and voltage. The sensor is based on a model of the open circuit voltage curve. This last model is implemented through monotonic neural networks and estimate over-potentials arising from the evolution in time of the Lithium concentration in the electrodes of the battery. The proposed soft sensor is able to exploit the information contained in operational records of the vehicle better than the alternatives, this being particularly true when the charge or discharge currents are between moderate and high. The accuracy of the neural model has been compared to different alternatives, including data-driven statistical models, first principle-based models, fuzzy observers and other recurrent neural networks with different topologies. It is concluded that monotonic echo state networks can outperform well established first-principle models. The algorithms have been validated with automotive Li-FePO4 cells.

  11. Archimedean copula estimation of distribution algorithm based on artificial bee colony algorithm

    Institute of Scientific and Technical Information of China (English)

    Haidong Xu; Mingyan Jiang; Kun Xu

    2015-01-01

    The artificial bee colony (ABC) algorithm is a com-petitive stochastic population-based optimization algorithm. How-ever, the ABC algorithm does not use the social information and lacks the knowledge of the problem structure, which leads to in-sufficiency in both convergent speed and searching precision. Archimedean copula estimation of distribution algorithm (ACEDA) is a relatively simple, time-economic and multivariate correlated EDA. This paper proposes a novel hybrid algorithm based on the ABC algorithm and ACEDA cal ed Archimedean copula estima-tion of distribution based on the artificial bee colony (ACABC) algorithm. The hybrid algorithm utilizes ACEDA to estimate the distribution model and then uses the information to help artificial bees to search more efficiently in the search space. Six bench-mark functions are introduced to assess the performance of the ACABC algorithm on numerical function optimization. Experimen-tal results show that the ACABC algorithm converges much faster with greater precision compared with the ABC algorithm, ACEDA and the global best (gbest)-guided ABC (GABC) algorithm in most of the experiments.

  12. Models and algorithms for midterm production planning under uncertainty: application of proximal decomposition methods

    International Nuclear Information System (INIS)

    Lenoir, A.

    2008-01-01

    We focus in this thesis, on the optimization process of large systems under uncertainty, and more specifically on solving the class of so-called deterministic equivalents with the help of splitting methods. The underlying application we have in mind is the electricity unit commitment problem under climate, market and energy consumption randomness, arising at EDF. We set the natural time-space-randomness couplings related to this application and we propose two new discretization schemes to tackle the randomness one, each of them based on non-parametric estimation of conditional expectations. This constitute an alternative to the usual scenario tree construction. We use the mathematical model consisting of the sum of two convex functions, a separable one and a coupling one. On the one hand, this simplified model offers a general framework to study decomposition-coordination algorithms by elapsing technicality due to a particular choice of subsystems. On the other hand, the convexity assumption allows to take advantage of monotone operators theory and to identify proximal methods as fixed point algorithms. We underlie the differential properties of the generalized reactions we are looking for a fixed point in order to derive bounds on the speed of convergence. Then we examine two families of decomposition-coordination algorithms resulting from operator splitting methods, namely Forward-Backward and Rachford methods. We suggest some practical method of acceleration of the Rachford class methods. To this end, we analyze the method from a theoretical point of view, furnishing as a byproduct explanations to some numerical observations. Then we propose as a response some improvements. Among them, an automatic updating strategy of scaling factors can correct a potential bad initial choice. The convergence proof is made easier thanks to stability results of some operator composition with respect to graphical convergence provided before. We also submit the idea of introducing

  13. A Survey on Operator Monotonicity, Operator Convexity, and Operator Means

    Directory of Open Access Journals (Sweden)

    Pattrawut Chansangiam

    2015-01-01

    Full Text Available This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.

  14. On the Convergence of Biogeography-Based Optimization for Binary Problems

    Directory of Open Access Journals (Sweden)

    Haiping Ma

    2014-01-01

    Full Text Available Biogeography-based optimization (BBO is an evolutionary algorithm inspired by biogeography, which is the study of the migration of species between habitats. A finite Markov chain model of BBO for binary problems was derived in earlier work, and some significant theoretical results were obtained. This paper analyzes the convergence properties of BBO on binary problems based on the previously derived BBO Markov chain model. Analysis reveals that BBO with only migration and mutation never converges to the global optimum. However, BBO with elitism, which maintains the best candidate in the population from one generation to the next, converges to the global optimum. In spite of previously published differences between genetic algorithms (GAs and BBO, this paper shows that the convergence properties of BBO are similar to those of the canonical GA. In addition, the convergence rate estimate of BBO with elitism is obtained in this paper and is confirmed by simulations for some simple representative problems.

  15. Iterative methods used in overlap astrometric reduction techniques do not always converge

    Science.gov (United States)

    Rapaport, M.; Ducourant, C.; Colin, J.; Le Campion, J. F.

    1993-04-01

    In this paper we prove that the classical Gauss-Seidel type iterative methods used for the solution of the reduced normal equations occurring in overlapping reduction methods of astrometry do not always converge. We exhibit examples of divergence. We then analyze an alternative algorithm proposed by Wang (1985). We prove the consistency of this algorithm and verify that it can be convergent while the Gauss-Seidel method is divergent. We conjecture the convergence of Wang method for the solution of astrometric problems using overlap techniques.

  16. Convergent validity test, construct validity test and external validity test of the David Liberman algorithm

    Directory of Open Access Journals (Sweden)

    David Maldavsky

    2013-08-01

    Full Text Available The author first exposes a complement of a previous test about convergent validity, then a construct validity test and finally an external validity test of the David Liberman algorithm.  The first part of the paper focused on a complementary aspect, the differential sensitivity of the DLA 1 in an external comparison (to other methods, and 2 in an internal comparison (between two ways of using the same method, the DLA.  The construct validity test exposes the concepts underlined to DLA, their operationalization and some corrections emerging from several empirical studies we carried out.  The external validity test examines the possibility of using the investigation of a single case and its relation with the investigation of a more extended sample.

  17. Logarithmically completely monotonic functions involving the Generalized Gamma Function

    OpenAIRE

    Faton Merovci; Valmir Krasniqi

    2010-01-01

    By a simple approach, two classes of functions involving generalization Euler's gamma function and originating from certain  problems of traffic flow are proved to be logarithmically  completely monotonic and a class of functions involving the psi function is showed to be completely monotonic.

  18. Fractal aspects and convergence of Newton`s method

    Energy Technology Data Exchange (ETDEWEB)

    Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)

    1996-12-31

    Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.

  19. Monotonic Loading of Circular Surface Footings on Clay

    DEFF Research Database (Denmark)

    Ibsen, Lars Bo; Barari, Amin

    2011-01-01

    Appropriate modeling of offshore foundations under monotonic loading is a significant challenge in geotechnical engineering. This paper reports experimental and numerical analyses, specifically investigating the response of circular surface footings during monotonic loading and elastoplastic...... behavior during reloading. By using the findings presented in this paper, it is possible to extend the model to simulate the vertical-load displacement response of offshore bucket foundations....

  20. Frequency-Domain Adaptive Algorithm for Network Echo Cancellation in VoIP

    Directory of Open Access Journals (Sweden)

    Patrick A. Naylor

    2008-05-01

    Full Text Available We propose a new low complexity, low delay, and fast converging frequency-domain adaptive algorithm for network echo cancellation in VoIP exploiting MMax and sparse partial (SP tap-selection criteria in the frequency domain. We incorporate these tap-selection techniques into the multidelay filtering (MDF algorithm in order to mitigate the delay inherent in frequency-domain algorithms. We illustrate two such approaches and discuss their tradeoff between convergence performance and computational complexity. Simulation results show an improvement in convergence rate for the proposed algorithm over MDF and significantly reduced complexity. The proposed algorithm achieves a convergence performance close to that of the recently proposed, but substantially more complex improved proportionate MDF (IPMDF algorithm.

  1. Convergence Analysis of a Class of Computational Intelligence Approaches

    Directory of Open Access Journals (Sweden)

    Junfeng Chen

    2013-01-01

    Full Text Available Computational intelligence approaches is a relatively new interdisciplinary field of research with many promising application areas. Although the computational intelligence approaches have gained huge popularity, it is difficult to analyze the convergence. In this paper, a computational model is built up for a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization, and particle swarm optimization in order to describe the common features of these algorithms. And then, two quantification indices, that is, the variation rate and the progress rate, are defined, respectively, to indicate the variety and the optimality of the solution sets generated in the search process of the model. Moreover, we give four types of probabilistic convergence for the solution set updating sequences, and their relations are discussed. Finally, the sufficient conditions are derived for the almost sure weak convergence and the almost sure strong convergence of the model by introducing the martingale theory into the Markov chain analysis.

  2. Proofs with monotone cuts

    Czech Academy of Sciences Publication Activity Database

    Jeřábek, Emil

    2012-01-01

    Roč. 58, č. 3 (2012), s. 177-187 ISSN 0942-5616 R&D Projects: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545 Institutional support: RVO:67985840 Keywords : proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.376, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/malq.201020071/full

  3. A Self-Adaptive Fuzzy c-Means Algorithm for Determining the Optimal Number of Clusters

    Science.gov (United States)

    Wang, Zhihao; Yi, Jing

    2016-01-01

    For the shortcoming of fuzzy c-means algorithm (FCM) needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rule n and obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup 1999, and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result. PMID:28042291

  4. Logarithmically completely monotonic functions involving the Generalized Gamma Function

    Directory of Open Access Journals (Sweden)

    Faton Merovci

    2010-12-01

    Full Text Available By a simple approach, two classes of functions involving generalization Euler's gamma function and originating from certain  problems of traffic flow are proved to be logarithmically  completely monotonic and a class of functions involving the psi function is showed to be completely monotonic.

  5. A fast iterative soft-thresholding algorithm for few-view CT reconstruction

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Junfeng; Mou, Xuanqin; Zhang, Yanbo [Jiaotong Univ., Xi' an (China). Inst. of Image Processing and Pattern Recognition

    2011-07-01

    Iterative soft-thresholding algorithms with total variation regularization can produce high-quality reconstructions from few views and even in the presence of noise. However, these algorithms are known to converge quite slowly, with a proven theoretically global convergence rate O(1/k), where k is iteration number. In this paper, we present a fast iterative soft-thresholding algorithm for few-view fan beam CT reconstruction with a global convergence rate O(1/k{sup 2}), which is significantly faster than the iterative soft-thresholding algorithm. Simulation results demonstrate the superior performance of the proposed algorithm in terms of convergence speed and reconstruction quality. (orig.)

  6. Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions

    CERN Document Server

    Michel, Anthony N; Liu, Derong

    2015-01-01

    The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.  For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks.   The authors cover the following four general topics:   -          Representation and modeling of dynamical systems of the types described above -          Presentation of Lyapunov and Lagrange stability theory for dynamical sy...

  7. An improved VSS NLMS algorithm for active noise cancellation

    Science.gov (United States)

    Sun, Yunzhuo; Wang, Mingjiang; Han, Yufei; Zhang, Congyan

    2017-08-01

    In this paper, an improved variable step size NLMS algorithm is proposed. NLMS has fast convergence rate and low steady state error compared to other traditional adaptive filtering algorithm. But there is a contradiction between the convergence speed and steady state error that affect the performance of the NLMS algorithm. Now, we propose a new variable step size NLMS algorithm. It dynamically changes the step size according to current error and iteration times. The proposed algorithm has simple formulation and easily setting parameters, and effectively solves the contradiction in NLMS. The simulation results show that the proposed algorithm has a good tracking ability, fast convergence rate and low steady state error simultaneously.

  8. A new proof for the convergent iterative solution of the degenerate quantum double-well potential and its generalization

    International Nuclear Information System (INIS)

    Friedberg, R.; Lee, T.D.

    2003-01-01

    We present a new and simpler proof for the convergent iterative solution of the one-dimensional degenerate double-well potential. This new proof depends on a general theorem, called the hierarchy theorem, that shows the successive stages in the iteration to form a monotonically increasing sequence of approximations to the energy and to the wavefunction at any point x. This important property makes possible a much simpler proof of convergence than the one given before in the literature. The hierarchy theorem proven in this paper is applicable to a much wider class of potentials which includes the quartic potential

  9. Obliquely Propagating Non-Monotonic Double Layer in a Hot Magnetized Plasma

    International Nuclear Information System (INIS)

    Kim, T.H.; Kim, S.S.; Hwang, J.H.; Kim, H.Y.

    2005-01-01

    Obliquely propagating non-monotonic double layer is investigated in a hot magnetized plasma, which consists of a positively charged hot ion fluid and trapped, as well as free electrons. A model equation (modified Korteweg-de Vries equation) is derived by the usual reductive perturbation method from a set of basic hydrodynamic equations. A time stationary obliquely propagating non-monotonic double layer solution is obtained in a hot magnetized-plasma. This solution is an analytic extension of the monotonic double layer and the solitary hole. The effects of obliqueness, external magnetic field and ion temperature on the properties of the non-monotonic double layer are discussed

  10. POLARIZED LINE FORMATION IN NON-MONOTONIC VELOCITY FIELDS

    Energy Technology Data Exchange (ETDEWEB)

    Sampoorna, M.; Nagendra, K. N., E-mail: sampoorna@iiap.res.in, E-mail: knn@iiap.res.in [Indian Institute of Astrophysics, Koramangala, Bengaluru 560034 (India)

    2016-12-10

    For a correct interpretation of the observed spectro-polarimetric data from astrophysical objects such as the Sun, it is necessary to solve the polarized line transfer problems taking into account a realistic temperature structure, the dynamical state of the atmosphere, a realistic scattering mechanism (namely, the partial frequency redistribution—PRD), and the magnetic fields. In a recent paper, we studied the effects of monotonic vertical velocity fields on linearly polarized line profiles formed in isothermal atmospheres with and without magnetic fields. However, in general the velocity fields that prevail in dynamical atmospheres of astrophysical objects are non-monotonic. Stellar atmospheres with shocks, multi-component supernova atmospheres, and various kinds of wave motions in solar and stellar atmospheres are examples of non-monotonic velocity fields. Here we present studies on the effect of non-relativistic non-monotonic vertical velocity fields on the linearly polarized line profiles formed in semi-empirical atmospheres. We consider a two-level atom model and PRD scattering mechanism. We solve the polarized transfer equation in the comoving frame (CMF) of the fluid using a polarized accelerated lambda iteration method that has been appropriately modified for the problem at hand. We present numerical tests to validate the CMF method and also discuss the accuracy and numerical instabilities associated with it.

  11. A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming

    National Research Council Canada - National Science Library

    Ye, Y; Gueler, O; Tapia, Richard A; Zhang, Y

    1991-01-01

    ...)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap...

  12. The Orthogonally Partitioned EM Algorithm: Extending the EM Algorithm for Algorithmic Stability and Bias Correction Due to Imperfect Data.

    Science.gov (United States)

    Regier, Michael D; Moodie, Erica E M

    2016-05-01

    We propose an extension of the EM algorithm that exploits the common assumption of unique parameterization, corrects for biases due to missing data and measurement error, converges for the specified model when standard implementation of the EM algorithm has a low probability of convergence, and reduces a potentially complex algorithm into a sequence of smaller, simpler, self-contained EM algorithms. We use the theory surrounding the EM algorithm to derive the theoretical results of our proposal, showing that an optimal solution over the parameter space is obtained. A simulation study is used to explore the finite sample properties of the proposed extension when there is missing data and measurement error. We observe that partitioning the EM algorithm into simpler steps may provide better bias reduction in the estimation of model parameters. The ability to breakdown a complicated problem in to a series of simpler, more accessible problems will permit a broader implementation of the EM algorithm, permit the use of software packages that now implement and/or automate the EM algorithm, and make the EM algorithm more accessible to a wider and more general audience.

  13. Composite Differential Search Algorithm

    Directory of Open Access Journals (Sweden)

    Bo Liu

    2014-01-01

    Full Text Available Differential search algorithm (DS is a relatively new evolutionary algorithm inspired by the Brownian-like random-walk movement which is used by an organism to migrate. It has been verified to be more effective than ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES. In this paper, we propose four improved solution search algorithms, namely “DS/rand/1,” “DS/rand/2,” “DS/current to rand/1,” and “DS/current to rand/2” to search the new space and enhance the convergence rate for the global optimization problem. In order to verify the performance of different solution search methods, 23 benchmark functions are employed. Experimental results indicate that the proposed algorithm performs better than, or at least comparable to, the original algorithm when considering the quality of the solution obtained. However, these schemes cannot still achieve the best solution for all functions. In order to further enhance the convergence rate and the diversity of the algorithm, a composite differential search algorithm (CDS is proposed in this paper. This new algorithm combines three new proposed search schemes including “DS/rand/1,” “DS/rand/2,” and “DS/current to rand/1” with three control parameters using a random method to generate the offspring. Experiment results show that CDS has a faster convergence rate and better search ability based on the 23 benchmark functions.

  14. Monotonicity of social welfare optima

    DEFF Research Database (Denmark)

    Hougaard, Jens Leth; Østerdal, Lars Peter Raahave

    2010-01-01

    This paper considers the problem of maximizing social welfare subject to participation constraints. It is shown that for an income allocation method that maximizes a social welfare function there is a monotonic relationship between the incomes allocated to individual agents in a given coalition...

  15. Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks

    Directory of Open Access Journals (Sweden)

    Heng-you Lan

    2013-01-01

    Full Text Available We introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.

  16. Genetic Algorithm Applied to the Eigenvalue Equalization Filtered-x LMS Algorithm (EE-FXLMS

    Directory of Open Access Journals (Sweden)

    Stephan P. Lovstedt

    2008-01-01

    Full Text Available The FXLMS algorithm, used extensively in active noise control (ANC, exhibits frequency-dependent convergence behavior. This leads to degraded performance for time-varying tonal noise and noise with multiple stationary tones. Previous work by the authors proposed the eigenvalue equalization filtered-x least mean squares (EE-FXLMS algorithm. For that algorithm, magnitude coefficients of the secondary path transfer function are modified to decrease variation in the eigenvalues of the filtered-x autocorrelation matrix, while preserving the phase, giving faster convergence and increasing overall attenuation. This paper revisits the EE-FXLMS algorithm, using a genetic algorithm to find magnitude coefficients that give the least variation in eigenvalues. This method overcomes some of the problems with implementing the EE-FXLMS algorithm arising from finite resolution of sampled systems. Experimental control results using the original secondary path model, and a modified secondary path model for both the previous implementation of EE-FXLMS and the genetic algorithm implementation are compared.

  17. A cascadic monotonic time-discretized algorithm for finite-level quantum control computation

    Science.gov (United States)

    Ditz, P.; Borzi`, A.

    2008-03-01

    A computer package (CNMS) is presented aimed at the solution of finite-level quantum optimal control problems. This package is based on a recently developed computational strategy known as monotonic schemes. Quantum optimal control problems arise in particular in quantum optics where the optimization of a control representing laser pulses is required. The purpose of the external control field is to channel the system's wavefunction between given states in its most efficient way. Physically motivated constraints, such as limited laser resources, are accommodated through appropriately chosen cost functionals. Program summaryProgram title: CNMS Catalogue identifier: ADEB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 770 No. of bytes in distributed program, including test data, etc.: 7098 Distribution format: tar.gz Programming language: MATLAB 6 Computer: AMD Athlon 64 × 2 Dual, 2:21 GHz, 1:5 GB RAM Operating system: Microsoft Windows XP Word size: 32 Classification: 4.9 Nature of problem: Quantum control Solution method: Iterative Running time: 60-600 sec

  18. Noise can speed convergence in Markov chains.

    Science.gov (United States)

    Franzke, Brandon; Kosko, Bart

    2011-10-01

    A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.

  19. Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM

    OpenAIRE

    Zhang, Teng; Wu, Kanzhi; Song, Jingwei; Huang, Shoudong; Dissanayake, Gamini

    2017-01-01

    In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation...

  20. Approximation by Chebyshevian Bernstein Operators versus Convergence of Dimension Elevation

    KAUST Repository

    Ait-Haddou, Rachid; Mazure, Marie-Laurence

    2016-01-01

    On a closed bounded interval, consider a nested sequence of Extended Chebyshev spaces possessing Bernstein bases. This situation automatically generates an infinite dimension elevation algorithm transforming control polygons of any given level into control polygons of the next level. The convergence of these infinite sequences of polygons towards the corresponding curves is a classical issue in computer-aided geometric design. Moreover, according to recent work proving the existence of Bernstein-type operators in such Extended Chebyshev spaces, this nested sequence is automatically associated with an infinite sequence of Bernstein operators which all reproduce the same two-dimensional space. Whether or not this sequence of operators converges towards the identity on the space of all continuous functions is a natural issue in approximation theory. In the present article, we prove that the two issues are actually equivalent. Not only is this result interesting on the theoretical side, but it also has practical implications. For instance, it provides us with a Korovkin-type theorem of convergence of any infinite dimension elevation algorithm. It also enables us to tackle the question of convergence of the dimension elevation algorithm for any nested sequence obtained by repeated integration of the kernel of a given linear differential operator with constant coefficients. © 2016 Springer Science+Business Media New York

  1. Approximation by Chebyshevian Bernstein Operators versus Convergence of Dimension Elevation

    KAUST Repository

    Ait-Haddou, Rachid

    2016-03-18

    On a closed bounded interval, consider a nested sequence of Extended Chebyshev spaces possessing Bernstein bases. This situation automatically generates an infinite dimension elevation algorithm transforming control polygons of any given level into control polygons of the next level. The convergence of these infinite sequences of polygons towards the corresponding curves is a classical issue in computer-aided geometric design. Moreover, according to recent work proving the existence of Bernstein-type operators in such Extended Chebyshev spaces, this nested sequence is automatically associated with an infinite sequence of Bernstein operators which all reproduce the same two-dimensional space. Whether or not this sequence of operators converges towards the identity on the space of all continuous functions is a natural issue in approximation theory. In the present article, we prove that the two issues are actually equivalent. Not only is this result interesting on the theoretical side, but it also has practical implications. For instance, it provides us with a Korovkin-type theorem of convergence of any infinite dimension elevation algorithm. It also enables us to tackle the question of convergence of the dimension elevation algorithm for any nested sequence obtained by repeated integration of the kernel of a given linear differential operator with constant coefficients. © 2016 Springer Science+Business Media New York

  2. Convergence of a random walk method for the Burgers equation

    International Nuclear Information System (INIS)

    Roberts, S.

    1985-10-01

    In this paper we consider a random walk algorithm for the solution of Burgers' equation. The algorithm uses the method of fractional steps. The non-linear advection term of the equation is solved by advecting ''fluid'' particles in a velocity field induced by the particles. The diffusion term of the equation is approximated by adding an appropriate random perturbation to the positions of the particles. Though the algorithm is inefficient as a method for solving Burgers' equation, it does model a similar method, the random vortex method, which has been used extensively to solve the incompressible Navier-Stokes equations. The purpose of this paper is to demonstrate the strong convergence of our random walk method and so provide a model for the proof of convergence for more complex random walk algorithms; for instance, the random vortex method without boundaries

  3. Model-Free Adaptive Control Algorithm with Data Dropout Compensation

    Directory of Open Access Journals (Sweden)

    Xuhui Bu

    2012-01-01

    Full Text Available The convergence of model-free adaptive control (MFAC algorithm can be guaranteed when the system is subject to measurement data dropout. The system output convergent speed gets slower as dropout rate increases. This paper proposes a MFAC algorithm with data compensation. The missing data is first estimated using the dynamical linearization method, and then the estimated value is introduced to update control input. The convergence analysis of the proposed MFAC algorithm is given, and the effectiveness is also validated by simulations. It is shown that the proposed algorithm can compensate the effect of the data dropout, and the better output performance can be obtained.

  4. Quick fuzzy backpropagation algorithm.

    Science.gov (United States)

    Nikov, A; Stoeva, S

    2001-03-01

    A modification of the fuzzy backpropagation (FBP) algorithm called QuickFBP algorithm is proposed, where the computation of the net function is significantly quicker. It is proved that the FBP algorithm is of exponential time complexity, while the QuickFBP algorithm is of polynomial time complexity. Convergence conditions of the QuickFBP, resp. the FBP algorithm are defined and proved for: (1) single output neural networks in case of training patterns with different targets; and (2) multiple output neural networks in case of training patterns with equivalued target vector. They support the automation of the weights training process (quasi-unsupervised learning) establishing the target value(s) depending on the network's input values. In these cases the simulation results confirm the convergence of both algorithms. An example with a large-sized neural network illustrates the significantly greater training speed of the QuickFBP rather than the FBP algorithm. The adaptation of an interactive web system to users on the basis of the QuickFBP algorithm is presented. Since the QuickFBP algorithm ensures quasi-unsupervised learning, this implies its broad applicability in areas of adaptive and adaptable interactive systems, data mining, etc. applications.

  5. Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method

    KAUST Repository

    Cagnetti, Filippo; Gomes, Diogo A.; Tran, Hung Vinh

    2013-01-01

    We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.

  6. Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method

    KAUST Repository

    Cagnetti, Filippo

    2013-11-01

    We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.

  7. Modified artificial bee colony algorithm for reactive power optimization

    Science.gov (United States)

    Sulaiman, Noorazliza; Mohamad-Saleh, Junita; Abro, Abdul Ghani

    2015-05-01

    Bio-inspired algorithms (BIAs) implemented to solve various optimization problems have shown promising results which are very important in this severely complex real-world. Artificial Bee Colony (ABC) algorithm, a kind of BIAs has demonstrated tremendous results as compared to other optimization algorithms. This paper presents a new modified ABC algorithm referred to as JA-ABC3 with the aim to enhance convergence speed and avoid premature convergence. The proposed algorithm has been simulated on ten commonly used benchmarks functions. Its performance has also been compared with other existing ABC variants. To justify its robust applicability, the proposed algorithm has been tested to solve Reactive Power Optimization problem. The results have shown that the proposed algorithm has superior performance to other existing ABC variants e.g. GABC, BABC1, BABC2, BsfABC dan IABC in terms of convergence speed. Furthermore, the proposed algorithm has also demonstrated excellence performance in solving Reactive Power Optimization problem.

  8. Convergence Properties of Projection and Contraction Methods for Variational Inequality Problems

    International Nuclear Information System (INIS)

    Xiu, N.; Wang, C.; Zhang, J.

    2001-01-01

    In this paper we develop the convergence theory of a general class of projection and contraction algorithms (PC method), where an extended stepsize rule is used, for solving variational inequality (VI) problems. It is shown that, by defining a scaled projection residue, the PC method forces the sequence of the residues to zero. It is also shown that, by defining a projected function, the PC method forces the sequence of projected functions to zero. A consequence of this result is that if the PC method converges to a nondegenerate solution of the VI problem, then after a finite number of iterations, the optimal face is identified. Finally, we study local convergence behavior of the extragradient algorithm for solving the KKT system of the inequality constrained VI problem

  9. Analysis of Known Linear Distributed Average Consensus Algorithms on Cycles and Paths

    Directory of Open Access Journals (Sweden)

    Jesús Gutiérrez-Gutiérrez

    2018-03-01

    Full Text Available In this paper, we compare six known linear distributed average consensus algorithms on a sensor network in terms of convergence time (and therefore, in terms of the number of transmissions required. The selected network topologies for the analysis (comparison are the cycle and the path. Specifically, in the present paper, we compute closed-form expressions for the convergence time of four known deterministic algorithms and closed-form bounds for the convergence time of two known randomized algorithms on cycles and paths. Moreover, we also compute a closed-form expression for the convergence time of the fastest deterministic algorithm considered on grids.

  10. Information flow in layered networks of non-monotonic units

    International Nuclear Information System (INIS)

    Neves, Fabio Schittler; Schubert, Benno Martim; Erichsen, Rubem Jr

    2015-01-01

    Layered neural networks are feedforward structures that yield robust parallel and distributed pattern recognition. Even though much attention has been paid to pattern retrieval properties in such systems, many aspects of their dynamics are not yet well characterized or understood. In this work we study, at different temperatures, the memory activity and information flows through layered networks in which the elements are the simplest binary odd non-monotonic function. Our results show that, considering a standard Hebbian learning approach, the network information content has its maximum always at the monotonic limit, even though the maximum memory capacity can be found at non-monotonic values for small enough temperatures. Furthermore, we show that such systems exhibit rich macroscopic dynamics, including not only fixed point solutions of its iterative map, but also cyclic and chaotic attractors that also carry information. (paper)

  11. Information flow in layered networks of non-monotonic units

    Science.gov (United States)

    Schittler Neves, Fabio; Martim Schubert, Benno; Erichsen, Rubem, Jr.

    2015-07-01

    Layered neural networks are feedforward structures that yield robust parallel and distributed pattern recognition. Even though much attention has been paid to pattern retrieval properties in such systems, many aspects of their dynamics are not yet well characterized or understood. In this work we study, at different temperatures, the memory activity and information flows through layered networks in which the elements are the simplest binary odd non-monotonic function. Our results show that, considering a standard Hebbian learning approach, the network information content has its maximum always at the monotonic limit, even though the maximum memory capacity can be found at non-monotonic values for small enough temperatures. Furthermore, we show that such systems exhibit rich macroscopic dynamics, including not only fixed point solutions of its iterative map, but also cyclic and chaotic attractors that also carry information.

  12. Transformation-invariant and nonparametric monotone smooth estimation of ROC curves.

    Science.gov (United States)

    Du, Pang; Tang, Liansheng

    2009-01-30

    When a new diagnostic test is developed, it is of interest to evaluate its accuracy in distinguishing diseased subjects from non-diseased subjects. The accuracy of the test is often evaluated by receiver operating characteristic (ROC) curves. Smooth ROC estimates are often preferable for continuous test results when the underlying ROC curves are in fact continuous. Nonparametric and parametric methods have been proposed by various authors to obtain smooth ROC curve estimates. However, there are certain drawbacks with the existing methods. Parametric methods need specific model assumptions. Nonparametric methods do not always satisfy the inherent properties of the ROC curves, such as monotonicity and transformation invariance. In this paper we propose a monotone spline approach to obtain smooth monotone ROC curves. Our method ensures important inherent properties of the underlying ROC curves, which include monotonicity, transformation invariance, and boundary constraints. We compare the finite sample performance of the newly proposed ROC method with other ROC smoothing methods in large-scale simulation studies. We illustrate our method through a real life example. Copyright (c) 2008 John Wiley & Sons, Ltd.

  13. Performance Analyses of IDEAL Algorithm on Highly Skewed Grid System

    Directory of Open Access Journals (Sweden)

    Dongliang Sun

    2014-03-01

    Full Text Available IDEAL is an efficient segregated algorithm for the fluid flow and heat transfer problems. This algorithm has now been extended to the 3D nonorthogonal curvilinear coordinates. Highly skewed grids in the nonorthogonal curvilinear coordinates can decrease the convergence rate and deteriorate the calculating stability. In this study, the feasibility of the IDEAL algorithm on highly skewed grid system is analyzed by investigating the lid-driven flow in the inclined cavity. It can be concluded that the IDEAL algorithm is more robust and more efficient than the traditional SIMPLER algorithm, especially for the highly skewed and fine grid system. For example, at θ = 5° and grid number = 70 × 70 × 70, the convergence rate of the IDEAL algorithm is 6.3 times faster than that of the SIMPLER algorithm, and the IDEAL algorithm can converge almost at any time step multiple.

  14. An Improved Harmony Search Algorithm for Power Distribution Network Planning

    Directory of Open Access Journals (Sweden)

    Wei Sun

    2015-01-01

    Full Text Available Distribution network planning because of involving many variables and constraints is a multiobjective, discrete, nonlinear, and large-scale optimization problem. Harmony search (HS algorithm is a metaheuristic algorithm inspired by the improvisation process of music players. HS algorithm has several impressive advantages, such as easy implementation, less adjustable parameters, and quick convergence. But HS algorithm still has some defects such as premature convergence and slow convergence speed. According to the defects of the standard algorithm and characteristics of distribution network planning, an improved harmony search (IHS algorithm is proposed in this paper. We set up a mathematical model of distribution network structure planning, whose optimal objective function is to get the minimum annual cost and constraint conditions are overload and radial network. IHS algorithm is applied to solve the complex optimization mathematical model. The empirical results strongly indicate that IHS algorithm can effectively provide better results for solving the distribution network planning problem compared to other optimization algorithms.

  15. Accurate and Fast Convergent Initial-Value Belief Propagation for Stereo Matching.

    Science.gov (United States)

    Wang, Xiaofeng; Liu, Yiguang

    2015-01-01

    The belief propagation (BP) algorithm has some limitations, including ambiguous edges and textureless regions, and slow convergence speed. To address these problems, we present a novel algorithm that intrinsically improves both the accuracy and the convergence speed of BP. First, traditional BP generally consumes time due to numerous iterations. To reduce the number of iterations, inspired by the crucial importance of the initial value in nonlinear problems, a novel initial-value belief propagation (IVBP) algorithm is presented, which can greatly improve both convergence speed and accuracy. Second, .the majority of the existing research on BP concentrates on the smoothness term or other energy terms, neglecting the significance of the data term. In this study, a self-adapting dissimilarity data term (SDDT) is presented to improve the accuracy of the data term, which incorporates an additional gradient-based measure into the traditional data term, with the weight determined by the robust measure-based control function. Finally, this study explores the effective combination of local methods and global methods. The experimental results have demonstrated that our method performs well compared with the state-of-the-art BP and simultaneously holds better edge-preserving smoothing effects with fast convergence speed in the Middlebury and new 2014 Middlebury datasets.

  16. Improved Bayesian optimization algorithm with fast convergence%一种快速收敛的改进贝叶斯优化算法

    Institute of Scientific and Technical Information of China (English)

    王翔; 郑建国; 张超群; 刘荣辉

    2011-01-01

    针对贝叶斯优化算法(BOA)中学习贝叶斯网络结构时间复杂度较高的问题,提出了一种可以快速收敛的基于K2的贝叶斯优化算法(K2-BOA).为了提升收敛速度,在学习贝叶斯网络结构的步骤中进行了2处改进:首先,随机生成n个变量的拓扑排序,加大了算法的随机性;其次,在排序的基础上利用K2算法学习贝叶斯网络结构,减少了整个算法的时问复杂度.针对3个标准Benchmark函数的仿真实验表明:采用K2-BOA算法和BOA算法解决简单分解函数问题时,寻找到最优值的适应度函数评价次数几乎相同,但是每次迭代K2-BOA算法运行速度提升明显;当解决比较复杂的6阶双极欺骗函数问题时,K2-BOA算法无论是运行时间还是适应度函数评价次数,都远小于BOA算法.%K2-Bayesian optimization algorithm (BOA) with fast convergence was proposed to enhance the convergence rate figuring out the problem that the time complexity of learning Bayesian networks was high in the Bayesian optimization algorithm. There were two improvements in learning Bayesian network of the new algorithm: the topological sort of n variables was randomly generated for increasing the randomness of the algorithm, and on the basis of the sort K2 algorithm was used to learn Bayesian network structure to reduce the time complexity of the new algorithm. The simulation results for three benchmark functions show two conclusions. Firstly, when 3-deceptive function and trap-5 function are solved, the number of fitness function evaluation of K2-Bayesian optimization algorithm is almost the same as that of Bayesian optimization algorithm; however the running time of K2-Bayesian optimization algorithm is less than that of Bayesian optimization algorithm. Secondly, when 6-bipolar function is solved, the number of fitness function evaluation and the running time of K2-Bayesian optimization algorithm are much better than those of Bayesian optimization algorithm.

  17. A theoretical analysis of the median LMF adaptive algorithm

    DEFF Research Database (Denmark)

    Bysted, Tommy Kristensen; Rusu, C.

    1999-01-01

    Higher order adaptive algorithms are sensitive to impulse interference. In the case of the LMF (Least Mean Fourth), an easy and effective way to reduce this is to median filter the instantaneous gradient of the LMF algorithm. Although previous published simulations have indicated that this reduces...... the speed of convergence, no analytical studies have yet been made to prove this. In order to enhance the usability, this paper presents a convergence and steady-state analysis of the median LMF adaptive algorithm. As expected this proves that the median LMF has a slower convergence and a lower steady...

  18. Parallel algorithms for nuclear reactor analysis via domain decomposition method

    International Nuclear Information System (INIS)

    Kim, Yong Hee

    1995-02-01

    In this thesis, the neutron diffusion equation in reactor physics is discretized by the finite difference method and is solved on a parallel computer network which is composed of T-800 transputers. T-800 transputer is a message-passing type MIMD (multiple instruction streams and multiple data streams) architecture. A parallel variant of Schwarz alternating procedure for overlapping subdomains is developed with domain decomposition. The thesis provides convergence analysis and improvement of the convergence of the algorithm. The convergence of the parallel Schwarz algorithms with DN(or ND), DD, NN, and mixed pseudo-boundary conditions(a weighted combination of Dirichlet and Neumann conditions) is analyzed for both continuous and discrete models in two-subdomain case and various underlying features are explored. The analysis shows that the convergence rate of the algorithm highly depends on the pseudo-boundary conditions and the theoretically best one is the mixed boundary conditions(MM conditions). Also it is shown that there may exist a significant discrepancy between continuous model analysis and discrete model analysis. In order to accelerate the convergence of the parallel Schwarz algorithm, relaxation in pseudo-boundary conditions is introduced and the convergence analysis of the algorithm for two-subdomain case is carried out. The analysis shows that under-relaxation of the pseudo-boundary conditions accelerates the convergence of the parallel Schwarz algorithm if the convergence rate without relaxation is negative, and any relaxation(under or over) decelerates convergence if the convergence rate without relaxation is positive. Numerical implementation of the parallel Schwarz algorithm on an MIMD system requires multi-level iterations: two levels for fixed source problems, three levels for eigenvalue problems. Performance of the algorithm turns out to be very sensitive to the iteration strategy. In general, multi-level iterations provide good performance when

  19. Reliable method for fission source convergence of Monte Carlo criticality calculation with Wielandt's method

    International Nuclear Information System (INIS)

    Yamamoto, Toshihiro; Miyoshi, Yoshinori

    2004-01-01

    A new algorithm of Monte Carlo criticality calculations for implementing Wielandt's method, which is one of acceleration techniques for deterministic source iteration methods, is developed, and the algorithm can be successfully implemented into MCNP code. In this algorithm, part of fission neutrons emitted during random walk processes are tracked within the current cycle, and thus a fission source distribution used in the next cycle spread more widely. Applying this method intensifies a neutron interaction effect even in a loosely-coupled array where conventional Monte Carlo criticality methods have difficulties, and a converged fission source distribution can be obtained with fewer cycles. Computing time spent for one cycle, however, increases because of tracking fission neutrons within the current cycle, which eventually results in an increase of total computing time up to convergence. In addition, statistical fluctuations of a fission source distribution in a cycle are worsened by applying Wielandt's method to Monte Carlo criticality calculations. However, since a fission source convergence is attained with fewer source iterations, a reliable determination of convergence can easily be made even in a system with a slow convergence. This acceleration method is expected to contribute to prevention of incorrect Monte Carlo criticality calculations. (author)

  20. Population SAMC vs SAMC: Convergence and Applications to Gene Selection Problems

    KAUST Repository

    Faming Liang, Mingqi Wu

    2013-01-01

    The Bayesian model selection approach has been adopted by more and more people when analyzing a large data. However, it is known that the reversible jump MCMC (RJMCMC) algorithm, which is perhaps the most popular MCMC algorithm for Bayesian model selection, is prone to get trapped into local modes when the model space is complex. The stochastic approximation Monte Carlo (SAMC) algorithm essentially overcomes the local trap problem suffered by conventional MCMC algorithms by introducing a self-adjusting mechanism based on the past samples. In this paper, we propose a population SAMC (Pop-SAMC) algorithm, which works on a population of SAMC chains and can make use of crossover operators from genetic algorithms to further improve its efficiency. Under mild conditions, we show the convergence of this algorithm. Comparing to the single chain SAMC algorithm, Pop-SAMC provides a more efficient self-adjusting mechanism and thus can converge faster. The effectiveness of Pop-SAMC for Bayesian model selection problems is examined through a change-point identification problem and a gene selection problem. The numerical results indicate that Pop-SAMC significantly outperforms both the single chain SAMC and RJMCMC.

  1. Recognition algorithms in knot theory

    International Nuclear Information System (INIS)

    Dynnikov, I A

    2003-01-01

    In this paper the problem of constructing algorithms for comparing knots and links is discussed. A survey of existing approaches and basic results in this area is given. In particular, diverse combinatorial methods for representing links are discussed, the Haken algorithm for recognizing a trivial knot (the unknot) and a scheme for constructing a general algorithm (using Haken's ideas) for comparing links are presented, an approach based on representing links by closed braids is described, the known algorithms for solving the word problem and the conjugacy problem for braid groups are described, and the complexity of the algorithms under consideration is discussed. A new method of combinatorial description of knots is given together with a new algorithm (based on this description) for recognizing the unknot by using a procedure for monotone simplification. In the conclusion of the paper several problems are formulated whose solution could help to advance towards the 'algorithmization' of knot theory

  2. Iterates of piecewise monotone mappings on an interval

    CERN Document Server

    Preston, Chris

    1988-01-01

    Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.

  3. Risk-Sensitive Control with Near Monotone Cost

    International Nuclear Information System (INIS)

    Biswas, Anup; Borkar, V. S.; Suresh Kumar, K.

    2010-01-01

    The infinite horizon risk-sensitive control problem for non-degenerate controlled diffusions is analyzed under a 'near monotonicity' condition on the running cost that penalizes large excursions of the process.

  4. On a correspondence between regular and non-regular operator monotone functions

    DEFF Research Database (Denmark)

    Gibilisco, P.; Hansen, Frank; Isola, T.

    2009-01-01

    We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information....

  5. An improved affine projection algorithm for active noise cancellation

    Science.gov (United States)

    Zhang, Congyan; Wang, Mingjiang; Han, Yufei; Sun, Yunzhuo

    2017-08-01

    Affine projection algorithm is a signal reuse algorithm, and it has a good convergence rate compared to other traditional adaptive filtering algorithm. There are two factors that affect the performance of the algorithm, which are step factor and the projection length. In the paper, we propose a new variable step size affine projection algorithm (VSS-APA). It dynamically changes the step size according to certain rules, so that it can get smaller steady-state error and faster convergence speed. Simulation results can prove that its performance is superior to the traditional affine projection algorithm and in the active noise control (ANC) applications, the new algorithm can get very good results.

  6. Failure mechanisms of closed-cell aluminum foam under monotonic and cyclic loading

    International Nuclear Information System (INIS)

    Amsterdam, E.; De Hosson, J.Th.M.; Onck, P.R.

    2006-01-01

    This paper concentrates on the differences in failure mechanisms of Alporas closed-cell aluminum foam under either monotonic or cyclic loading. The emphasis lies on aspects of crack nucleation and crack propagation in relation to the microstructure. The cell wall material consists of Al dendrites and an interdendritic network of Al 4 Ca and Al 22 CaTi 2 precipitates. In situ scanning electron microscopy monotonic tensile tests were performed on small samples to study crack nucleation and propagation. Digital image correlation was employed to map the strain in the cell wall on the characteristic microstructural length scale. Monotonic tensile tests and tension-tension fatigue tests were performed on larger samples to observe the overall fracture behavior and crack path in monotonic and cyclic loading. The crack nucleation and propagation path in both loading conditions are revealed and it can be concluded that during monotonic tension cracks nucleate in and propagate partly through the Al 4 Ca interdendritic network, whereas under cyclic loading cracks nucleate and propagate through the Al dendrites

  7. Robust stability analysis of adaptation algorithms for single perceptron.

    Science.gov (United States)

    Hui, S; Zak, S H

    1991-01-01

    The problem of robust stability and convergence of learning parameters of adaptation algorithms in a noisy environment for the single preceptron is addressed. The case in which the same input pattern is presented in the adaptation cycle is analyzed. The algorithm proposed is of the Widrow-Hoff type. It is concluded that this algorithm is robust. However, the weight vectors do not necessarily converge in the presence of measurement noise. A modified version of this algorithm in which the reduction factors are allowed to vary with time is proposed, and it is shown that this algorithm is robust and that the weight vectors converge in the presence of bounded noise. Only deterministic-type arguments are used in the analysis. An ultimate bound on the error in terms of a convex combination of the initial error and the bound on the noise is obtained.

  8. An Optimal Augmented Monotonic Tracking Controller for Aircraft Engines with Output Constraints

    Directory of Open Access Journals (Sweden)

    Jiakun Qin

    2017-01-01

    Full Text Available This paper proposes a novel min-max control scheme for aircraft engines, with the aim of transferring a set of regulated outputs between two set-points, while ensuring a set of auxiliary outputs remain within prescribed constraints. In view of this, an optimal augmented monotonic tracking controller (OAMTC is proposed, by considering a linear plant with input integration, to enhance the ability of the control system to reject uncertainty in system parameters and ensure no crossing limits. The key idea is to use the eigenvalue and eigenvector placement method and genetic algorithms to shape the output responses. The approach is validated by numerical simulation. The results show that the designed OAMTC controller can achieve a satisfactory dynamic and steady performance and keep the auxiliary outputs within constraints in the transient regime.

  9. Strong Convergence Theorems for Variational Inequalities and Split Equality Problem

    Directory of Open Access Journals (Sweden)

    Yu Jing Wu

    2013-01-01

    Full Text Available Let H1, H2, and H3 be real Hilbert spaces, let C⊆H1, Q⊆H2 be two nonempty closed convex sets, and let A:H1→H3, B:H2→H3 be two bounded linear operators. The split equality problem (SEP is to find x∈C, y∈Q such that Ax=By. Let H=H1×H2; consider f:H→H a contraction with coefficient 00, and M:H→H is a β-inverse strongly monotone mapping. Let 0<γ<γ̅/α, S=C×Q and G:H→H3 be defined by restricting to H1 is A and restricting to H2 is -B, that is, G has the matrix form G=[A,-B]. It is proved that the sequence {wn}={(xn,yn}⊆H generated by the iterative method wn+1=PS[αnγf(wn+(I-αnTPS(I-γnG*GPS(wn-λnMwn] converges strongly to w̃ which solves the SEP and the following variational inequality: 〈(T-λfw̃,w-w̃〉≥0 and 〈Mw̃,w-w̃〉≥0 for all w∈S. Moreover, if we take M=G*G:H→H,  γn=0, then M is a β-inverse strongly monotone mapping, and the sequence {wn} generated by the iterative method wn+1=αnγf(wn+(I-αnTPS(wn-λnG*Gwn converges strongly to w̃ which solves the SEP and the following variational inequality: 〈(T-λfw̃,w-w̃〉≥0 for all w∈S.

  10. Some nonlinear space decomposition algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)

    1996-12-31

    Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.

  11. Set-Membership Proportionate Affine Projection Algorithms

    Directory of Open Access Journals (Sweden)

    Stefan Werner

    2007-01-01

    Full Text Available Proportionate adaptive filters can improve the convergence speed for the identification of sparse systems as compared to their conventional counterparts. In this paper, the idea of proportionate adaptation is combined with the framework of set-membership filtering (SMF in an attempt to derive novel computationally efficient algorithms. The resulting algorithms attain an attractive faster converge for both situations of sparse and dispersive channels while decreasing the average computational complexity due to the data discerning feature of the SMF approach. In addition, we propose a rule that allows us to automatically adjust the number of past data pairs employed in the update. This leads to a set-membership proportionate affine projection algorithm (SM-PAPA having a variable data-reuse factor allowing a significant reduction in the overall complexity when compared with a fixed data-reuse factor. Reduced-complexity implementations of the proposed algorithms are also considered that reduce the dimensions of the matrix inversions involved in the update. Simulations show good results in terms of reduced number of updates, speed of convergence, and final mean-squared error.

  12. Completely monotonic functions related to logarithmic derivatives of entire functions

    DEFF Research Database (Denmark)

    Pedersen, Henrik Laurberg

    2011-01-01

    The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity...... of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given....

  13. Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Huiping Cao

    2014-01-01

    Full Text Available Schubert’s method is an extension of Broyden’s method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden’s method. In particular, Schubert’s method has been proved to be locally and q-superlinearly convergent. In this paper, we globalize Schubert’s method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.

  14. Escalated convergent artificial bee colony

    Science.gov (United States)

    Jadon, Shimpi Singh; Bansal, Jagdish Chand; Tiwari, Ritu

    2016-03-01

    Artificial bee colony (ABC) optimisation algorithm is a recent, fast and easy-to-implement population-based meta heuristic for optimisation. ABC has been proved a rival algorithm with some popular swarm intelligence-based algorithms such as particle swarm optimisation, firefly algorithm and ant colony optimisation. The solution search equation of ABC is influenced by a random quantity which helps its search process in exploration at the cost of exploitation. In order to find a fast convergent behaviour of ABC while exploitation capability is maintained, in this paper basic ABC is modified in two ways. First, to improve exploitation capability, two local search strategies, namely classical unidimensional local search and levy flight random walk-based local search are incorporated with ABC. Furthermore, a new solution search strategy, namely stochastic diffusion scout search is proposed and incorporated into the scout bee phase to provide more chance to abandon solution to improve itself. Efficiency of the proposed algorithm is tested on 20 benchmark test functions of different complexities and characteristics. Results are very promising and they prove it to be a competitive algorithm in the field of swarm intelligence-based algorithms.

  15. Principal component analysis networks and algorithms

    CERN Document Server

    Kong, Xiangyu; Duan, Zhansheng

    2017-01-01

    This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.

  16. Monotone numerical methods for finite-state mean-field games

    KAUST Repository

    Gomes, Diogo A.; Saude, Joao

    2017-01-01

    Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

  17. Monotone numerical methods for finite-state mean-field games

    KAUST Repository

    Gomes, Diogo A.

    2017-04-29

    Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

  18. High Performance Parallel Multigrid Algorithms for Unstructured Grids

    Science.gov (United States)

    Frederickson, Paul O.

    1996-01-01

    We describe a high performance parallel multigrid algorithm for a rather general class of unstructured grid problems in two and three dimensions. The algorithm PUMG, for parallel unstructured multigrid, is related in structure to the parallel multigrid algorithm PSMG introduced by McBryan and Frederickson, for they both obtain a higher convergence rate through the use of multiple coarse grids. Another reason for the high convergence rate of PUMG is its smoother, an approximate inverse developed by Baumgardner and Frederickson.

  19. Streaming Algorithms for Line Simplification

    DEFF Research Database (Denmark)

    Abam, Mohammad; de Berg, Mark; Hachenberger, Peter

    2010-01-01

    this problem in a streaming setting, where we only have a limited amount of storage, so that we cannot store all the points. We analyze the competitive ratio of our algorithms, allowing resource augmentation: we let our algorithm maintain a simplification with 2k (internal) points and compare the error of our...... simplification to the error of the optimal simplification with k points. We obtain the algorithms with O(1) competitive ratio for three cases: convex paths, where the error is measured using the Hausdorff distance (or Fréchet distance), xy-monotone paths, where the error is measured using the Hausdorff distance...... (or Fréchet distance), and general paths, where the error is measured using the Fréchet distance. In the first case the algorithm needs O(k) additional storage, and in the latter two cases the algorithm needs O(k 2) additional storage....

  20. Particle swarm genetic algorithm and its application

    International Nuclear Information System (INIS)

    Liu Chengxiang; Yan Changxiang; Wang Jianjun; Liu Zhenhai

    2012-01-01

    To solve the problems of slow convergence speed and tendency to fall into the local optimum of the standard particle swarm optimization while dealing with nonlinear constraint optimization problem, a particle swarm genetic algorithm is designed. The proposed algorithm adopts feasibility principle handles constraint conditions and avoids the difficulty of penalty function method in selecting punishment factor, generates initial feasible group randomly, which accelerates particle swarm convergence speed, and introduces genetic algorithm crossover and mutation strategy to avoid particle swarm falls into the local optimum Through the optimization calculation of the typical test functions, the results show that particle swarm genetic algorithm has better optimized performance. The algorithm is applied in nuclear power plant optimization, and the optimization results are significantly. (authors)

  1. Mathematical model and coordination algorithms for ensuring complex security of an organization

    Science.gov (United States)

    Novoseltsev, V. I.; Orlova, D. E.; Dubrovin, A. S.; Irkhin, V. P.

    2018-03-01

    The mathematical model of coordination when ensuring complex security of the organization is considered. On the basis of use of a method of casual search three types of algorithms of effective coordination adequate to mismatch level concerning security are developed: a coordination algorithm at domination of instructions of the coordinator; a coordination algorithm at domination of decisions of performers; a coordination algorithm at parity of interests of the coordinator and performers. Assessment of convergence of the algorithms considered above it was made by carrying out a computing experiment. The described algorithms of coordination have property of convergence in the sense stated above. And, the following regularity is revealed: than more simply in the structural relation the algorithm, for the smaller number of iterations is provided to those its convergence.

  2. A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations

    KAUST Repository

    Bagci, Hakan; Pasciak, Joseph E.; Sirenko, Kostyantyn

    2014-01-01

    We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.

  3. A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations

    KAUST Repository

    Bagci, Hakan

    2014-11-11

    We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.

  4. Recursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm.

    Science.gov (United States)

    Yu, Feng; Mao, Zhizhong; Yuan, Ping; He, Dakuo; Jia, Mingxing

    2017-09-01

    This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  5. A discrete wavelet spectrum approach for identifying non-monotonic trends in hydroclimate data

    Science.gov (United States)

    Sang, Yan-Fang; Sun, Fubao; Singh, Vijay P.; Xie, Ping; Sun, Jian

    2018-01-01

    The hydroclimatic process is changing non-monotonically and identifying its trends is a great challenge. Building on the discrete wavelet transform theory, we developed a discrete wavelet spectrum (DWS) approach for identifying non-monotonic trends in hydroclimate time series and evaluating their statistical significance. After validating the DWS approach using two typical synthetic time series, we examined annual temperature and potential evaporation over China from 1961-2013 and found that the DWS approach detected both the warming and the warming hiatus in temperature, and the reversed changes in potential evaporation. Further, the identified non-monotonic trends showed stable significance when the time series was longer than 30 years or so (i.e. the widely defined climate timescale). The significance of trends in potential evaporation measured at 150 stations in China, with an obvious non-monotonic trend, was underestimated and was not detected by the Mann-Kendall test. Comparatively, the DWS approach overcame the problem and detected those significant non-monotonic trends at 380 stations, which helped understand and interpret the spatiotemporal variability in the hydroclimatic process. Our results suggest that non-monotonic trends of hydroclimate time series and their significance should be carefully identified, and the DWS approach proposed has the potential for wide use in the hydrological and climate sciences.

  6. Statistical identifiability and convergence evaluation for nonlinear pharmacokinetic models with particle swarm optimization.

    Science.gov (United States)

    Kim, Seongho; Li, Lang

    2014-02-01

    The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiability of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  7. In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements

    Czech Academy of Sciences Publication Activity Database

    Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav

    2016-01-01

    Roč. 90, č. 1 (2016), s. 249-261 ISSN 0001-9054 Institutional support: RVO:67985840 Keywords : symmetric spaces * K-monotone symmetric Banach spaces * strict monotonicity * lower local uniform monotonicity Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2016 http://link.springer.com/article/10.1007%2Fs00010-015-0379-6

  8. Characterizing and improving generalized belief propagation algorithms on the 2D Edwards–Anderson model

    International Nuclear Information System (INIS)

    Domínguez, Eduardo; Lage-Castellanos, Alejandro; Mulet, Roberto; Ricci-Tersenghi, Federico; Rizzo, Tommaso

    2011-01-01

    We study the performance of different message passing algorithms in the two-dimensional Edwards–Anderson model. We show that the standard belief propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then, we test a generalized belief propagation (GBP) algorithm, derived from a cluster variational method (CVM) at the plaquette level. We compare its performance with BP and with other algorithms derived under the same approximation: double loop (DL) and a two-way message passing algorithm (HAK). The plaquette-CVM approximation improves BP in at least three ways: the quality of the paramagnetic solution at high temperatures, a better estimate (lower) for the critical temperature, and the fact that the GBP message passing algorithm converges also to nonparamagnetic solutions. The lack of convergence of the standard GBP message passing algorithm at low temperatures seems to be related to the implementation details and not to the appearance of long range order. In fact, we prove that a gauge invariance of the constrained CVM free energy can be exploited to derive a new message passing algorithm which converges at even lower temperatures. In all its region of convergence this new algorithm is faster than HAK and DL by some orders of magnitude

  9. Convergence analysis of neutronic/thermohydraulic coupling behavior of SCWR

    International Nuclear Information System (INIS)

    Liu, Shichang; Cai, Jiejin

    2013-01-01

    The neutronic/thermohydraulic coupling (N–T coupling) calculations play an important role in core design and stability analysis. The traditional iterative method is not applicable for some new reactors (such as supercritical water-cooled reactor) which have intense N–T coupling behavior. In this paper, the mathematical model of N–T coupling based on fixed point theory is established firstly, with the convergent criterion, which can show the real-time convergence situation of iteration. Secondly, the self-adaptive relaxation factor and corresponding algorithm are proposed. Thirdly, the convergence analysis of the method of self-adaptive relaxation factor and common relaxation iteration has been performed, based on three calculation examples of SCWR fuel assembly. The results show that the proposed algorithm can efficiently reduce the calculation time and be adapted to different coupling cases and different initial distribution. It is easy to program, providing convenience for reactor design and analysis. This research also provides the theoretical basis for further study of N–T coupling behavior of new reactors such as SCWR

  10. Alternans by non-monotonic conduction velocity restitution, bistability and memory

    International Nuclear Information System (INIS)

    Kim, Tae Yun; Hong, Jin Hee; Heo, Ryoun; Lee, Kyoung J

    2013-01-01

    Conduction velocity (CV) restitution is a key property that characterizes any medium supporting traveling waves. It reflects not only the dynamics of the individual constituents but also the coupling mechanism that mediates their interaction. Recent studies have suggested that cardiac tissues, which have a non-monotonic CV-restitution property, can support alternans, a period-2 oscillatory response of periodically paced cardiac tissue. This study finds that single-hump, non-monotonic, CV-restitution curves are a common feature of in vitro cultures of rat cardiac cells. We also find that the Fenton–Karma model, one of the well-established mathematical models of cardiac tissue, supports a very similar non-monotonic CV restitution in a physiologically relevant parameter regime. Surprisingly, the mathematical model as well as the cell cultures support bistability and show cardiac memory that tends to work against the generation of an alternans. Bistability was realized by adopting two different stimulation protocols, ‘S1S2’, which produces a period-1 wave train, and ‘alternans-pacing’, which favors a concordant alternans. Thus, we conclude that the single-hump non-monotonicity in the CV-restitution curve is not sufficient to guarantee a cardiac alternans, since cardiac memory interferes and the way the system is paced matters. (paper)

  11. Log-supermodularity of weight functions and the loading monotonicity of weighted insurance premiums

    OpenAIRE

    Hristo S. Sendov; Ying Wang; Ricardas Zitikis

    2010-01-01

    The paper is motivated by a problem concerning the monotonicity of insurance premiums with respect to their loading parameter: the larger the parameter, the larger the insurance premium is expected to be. This property, usually called loading monotonicity, is satisfied by premiums that appear in the literature. The increased interest in constructing new insurance premiums has raised a question as to what weight functions would produce loading-monotonic premiums. In this paper we demonstrate a...

  12. Estimating monotonic rates from biological data using local linear regression.

    Science.gov (United States)

    Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

    2017-03-01

    Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

  13. On the convergence of nonconvex minimization methods for image recovery.

    Science.gov (United States)

    Xiao, Jin; Ng, Michael Kwok-Po; Yang, Yu-Fei

    2015-05-01

    Nonconvex nonsmooth regularization method has been shown to be effective for restoring images with neat edges. Fast alternating minimization schemes have also been proposed and developed to solve the nonconvex nonsmooth minimization problem. The main contribution of this paper is to show the convergence of these alternating minimization schemes, based on the Kurdyka-Łojasiewicz property. In particular, we show that the iterates generated by the alternating minimization scheme, converges to a critical point of this nonconvex nonsmooth objective function. We also extend the analysis to nonconvex nonsmooth regularization model with box constraints, and obtain similar convergence results of the related minimization algorithm. Numerical examples are given to illustrate our convergence analysis.

  14. Recursive forgetting algorithms

    DEFF Research Database (Denmark)

    Parkum, Jens; Poulsen, Niels Kjølstad; Holst, Jan

    1992-01-01

    In the first part of the paper, a general forgetting algorithm is formulated and analysed. It contains most existing forgetting schemes as special cases. Conditions are given ensuring that the basic convergence properties will hold. In the second part of the paper, the results are applied...... to a specific algorithm with selective forgetting. Here, the forgetting is non-uniform in time and space. The theoretical analysis is supported by a simulation example demonstrating the practical performance of this algorithm...

  15. AMOBH: Adaptive Multiobjective Black Hole Algorithm.

    Science.gov (United States)

    Wu, Chong; Wu, Tao; Fu, Kaiyuan; Zhu, Yuan; Li, Yongbo; He, Wangyong; Tang, Shengwen

    2017-01-01

    This paper proposes a new multiobjective evolutionary algorithm based on the black hole algorithm with a new individual density assessment (cell density), called "adaptive multiobjective black hole algorithm" (AMOBH). Cell density has the characteristics of low computational complexity and maintains a good balance of convergence and diversity of the Pareto front. The framework of AMOBH can be divided into three steps. Firstly, the Pareto front is mapped to a new objective space called parallel cell coordinate system. Then, to adjust the evolutionary strategies adaptively, Shannon entropy is employed to estimate the evolution status. At last, the cell density is combined with a dominance strength assessment called cell dominance to evaluate the fitness of solutions. Compared with the state-of-the-art methods SPEA-II, PESA-II, NSGA-II, and MOEA/D, experimental results show that AMOBH has a good performance in terms of convergence rate, population diversity, population convergence, subpopulation obtention of different Pareto regions, and time complexity to the latter in most cases.

  16. A Hybrid Chaotic Quantum Evolutionary Algorithm

    DEFF Research Database (Denmark)

    Cai, Y.; Zhang, M.; Cai, H.

    2010-01-01

    A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form a pe...... tests. The presented algorithm is applied to urban traffic signal timing optimization and the effect is satisfied....

  17. Monotonicity and bounds on Bessel functions

    Directory of Open Access Journals (Sweden)

    Larry Landau

    2000-07-01

    Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.

  18. A note on a perfect simulation algorithm for marked Hawkes processes

    DEFF Research Database (Denmark)

    Møller, Jesper; Rasmussen, Jakob Gulddahl

    2004-01-01

    The usual straightforward simulation algorithm for (marked or unmarked) Hawkes processes suffers from edge effect. In this note we describe a perfect simulation algorithm which is partly derived as in Brix and Kendall (2002) and partly using upper and lower processes as in the Propp......-Wilson algorithm (1996), or rather as in the dominated CFTP algorithm by Kendall and Moller (2000). Various monotonicity properties and approximations of the cumulative distribution function for the length of a so-called cluster in a marked Hawkes process play an important role....

  19. A discrete wavelet spectrum approach for identifying non-monotonic trends in hydroclimate data

    Directory of Open Access Journals (Sweden)

    Y.-F. Sang

    2018-01-01

    Full Text Available The hydroclimatic process is changing non-monotonically and identifying its trends is a great challenge. Building on the discrete wavelet transform theory, we developed a discrete wavelet spectrum (DWS approach for identifying non-monotonic trends in hydroclimate time series and evaluating their statistical significance. After validating the DWS approach using two typical synthetic time series, we examined annual temperature and potential evaporation over China from 1961–2013 and found that the DWS approach detected both the warming and the warming hiatus in temperature, and the reversed changes in potential evaporation. Further, the identified non-monotonic trends showed stable significance when the time series was longer than 30 years or so (i.e. the widely defined climate timescale. The significance of trends in potential evaporation measured at 150 stations in China, with an obvious non-monotonic trend, was underestimated and was not detected by the Mann–Kendall test. Comparatively, the DWS approach overcame the problem and detected those significant non-monotonic trends at 380 stations, which helped understand and interpret the spatiotemporal variability in the hydroclimatic process. Our results suggest that non-monotonic trends of hydroclimate time series and their significance should be carefully identified, and the DWS approach proposed has the potential for wide use in the hydrological and climate sciences.

  20. Guaranteed convergence of the Hough transform

    Science.gov (United States)

    Soffer, Menashe; Kiryati, Nahum

    1995-01-01

    The straight-line Hough Transform using normal parameterization with a continuous voting kernel is considered. It transforms the colinearity detection problem to a problem of finding the global maximum of a two dimensional function above a domain in the parameter space. The principle is similar to robust regression using fixed scale M-estimation. Unlike standard M-estimation procedures the Hough Transform does not rely on a good initial estimate of the line parameters: The global optimization problem is approached by exhaustive search on a grid that is usually as fine as computationally feasible. The global maximum of a general function above a bounded domain cannot be found by a finite number of function evaluations. Only if sufficient a-priori knowledge about the smoothness of the objective function is available, convergence to the global maximum can be guaranteed. The extraction of a-priori information and its efficient use are the main challenges in real global optimization problems. The global optimization problem in the Hough Transform is essentially how fine should the parameter space quantization be in order not to miss the true maximum. More than thirty years after Hough patented the basic algorithm, the problem is still essentially open. In this paper an attempt is made to identify a-priori information on the smoothness of the objective (Hough) function and to introduce sufficient conditions for the convergence of the Hough Transform to the global maximum. An image model with several application dependent parameters is defined. Edge point location errors as well as background noise are accounted for. Minimal parameter space quantization intervals that guarantee convergence are obtained. Focusing policies for multi-resolution Hough algorithms are developed. Theoretical support for bottom- up processing is provided. Due to the randomness of errors and noise, convergence guarantees are probabilistic.

  1. The Algorithm for Algorithms: An Evolutionary Algorithm Based on Automatic Designing of Genetic Operators

    Directory of Open Access Journals (Sweden)

    Dazhi Jiang

    2015-01-01

    Full Text Available At present there is a wide range of evolutionary algorithms available to researchers and practitioners. Despite the great diversity of these algorithms, virtually all of the algorithms share one feature: they have been manually designed. A fundamental question is “are there any algorithms that can design evolutionary algorithms automatically?” A more complete definition of the question is “can computer construct an algorithm which will generate algorithms according to the requirement of a problem?” In this paper, a novel evolutionary algorithm based on automatic designing of genetic operators is presented to address these questions. The resulting algorithm not only explores solutions in the problem space like most traditional evolutionary algorithms do, but also automatically generates genetic operators in the operator space. In order to verify the performance of the proposed algorithm, comprehensive experiments on 23 well-known benchmark optimization problems are conducted. The results show that the proposed algorithm can outperform standard differential evolution algorithm in terms of convergence speed and solution accuracy which shows that the algorithm designed automatically by computers can compete with the algorithms designed by human beings.

  2. A new adaptive blind channel identification algorithm

    International Nuclear Information System (INIS)

    Peng Dezhong; Xiang Yong; Yi Zhang

    2009-01-01

    This paper addresses the blind identification of single-input multiple-output (SIMO) finite-impulse-response (FIR) systems. We first propose a new adaptive algorithm for the blind identification of SIMO FIR systems. Then, its convergence property is analyzed systematically. It is shown that under some mild conditions, the proposed algorithm is guaranteed to converge in the mean to the true channel impulse responses in both noisy and noiseless cases. Simulations are carried out to demonstrate the theoretical results.

  3. A note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method

    Directory of Open Access Journals (Sweden)

    Amir Fallahzadeh

    2014-07-01

    Full Text Available In this paper, the convergence of Zakharov-Kuznetsov (ZK equation by homotopy analysis method (HAM is investigated. A theorem is proved to guarantee the convergence of HAMand to find the series solution of this equation via a reliable algorithm.

  4. The Convergence Acceleration of Two-Dimensional Fourier Interpolation

    Directory of Open Access Journals (Sweden)

    Anry Nersessian

    2008-07-01

    Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.

  5. Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

    Science.gov (United States)

    Bui, Trong T.; Mankbadi, Reda R.

    1995-01-01

    Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

  6. Multimodal optimization by using hybrid of artificial bee colony algorithm and BFGS algorithm

    Science.gov (United States)

    Anam, S.

    2017-10-01

    Optimization has become one of the important fields in Mathematics. Many problems in engineering and science can be formulated into optimization problems. They maybe have many local optima. The optimization problem with many local optima, known as multimodal optimization problem, is how to find the global solution. Several metaheuristic methods have been proposed to solve multimodal optimization problems such as Particle Swarm Optimization (PSO), Genetics Algorithm (GA), Artificial Bee Colony (ABC) algorithm, etc. The performance of the ABC algorithm is better than or similar to those of other population-based algorithms with the advantage of employing a fewer control parameters. The ABC algorithm also has the advantages of strong robustness, fast convergence and high flexibility. However, it has the disadvantages premature convergence in the later search period. The accuracy of the optimal value cannot meet the requirements sometimes. Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is a good iterative method for finding a local optimum. Compared with other local optimization methods, the BFGS algorithm is better. Based on the advantages of the ABC algorithm and the BFGS algorithm, this paper proposes a hybrid of the artificial bee colony algorithm and the BFGS algorithm to solve the multimodal optimization problem. The first step is that the ABC algorithm is run to find a point. In the second step is that the point obtained by the first step is used as an initial point of BFGS algorithm. The results show that the hybrid method can overcome from the basic ABC algorithm problems for almost all test function. However, if the shape of function is flat, the proposed method cannot work well.

  7. An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup

    Directory of Open Access Journals (Sweden)

    Liu Min

    2010-01-01

    Full Text Available In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.

  8. A quasi-Newton algorithm for large-scale nonlinear equations

    Directory of Open Access Journals (Sweden)

    Linghua Huang

    2017-02-01

    Full Text Available Abstract In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i a conjugate gradient (CG algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm’s initial point does not have any restrictions; (ii a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length α k $\\alpha_{k}$ . The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the 1 + q $1+q$ -order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

  9. Diversity-Guided Evolutionary Algorithms

    DEFF Research Database (Denmark)

    Ursem, Rasmus Kjær

    2002-01-01

    Population diversity is undoubtably a key issue in the performance of evolutionary algorithms. A common hypothesis is that high diversity is important to avoid premature convergence and to escape local optima. Various diversity measures have been used to analyze algorithms, but so far few...... algorithms have used a measure to guide the search. The diversity-guided evolutionary algorithm (DGEA) uses the wellknown distance-to-average-point measure to alternate between phases of exploration (mutation) and phases of exploitation (recombination and selection). The DGEA showed remarkable results...

  10. Distributed weighted least-squares estimation with fast convergence for large-scale systems☆

    Science.gov (United States)

    Marelli, Damián Edgardo; Fu, Minyue

    2015-01-01

    In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976

  11. Distributed weighted least-squares estimation with fast convergence for large-scale systems.

    Science.gov (United States)

    Marelli, Damián Edgardo; Fu, Minyue

    2015-01-01

    In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.

  12. Optimal Pid Controller Design Using Adaptive Vurpso Algorithm

    Science.gov (United States)

    Zirkohi, Majid Moradi

    2015-04-01

    The purpose of this paper is to improve theVelocity Update Relaxation Particle Swarm Optimization algorithm (VURPSO). The improved algorithm is called Adaptive VURPSO (AVURPSO) algorithm. Then, an optimal design of a Proportional-Integral-Derivative (PID) controller is obtained using the AVURPSO algorithm. An adaptive momentum factor is used to regulate a trade-off between the global and the local exploration abilities in the proposed algorithm. This operation helps the system to reach the optimal solution quickly and saves the computation time. Comparisons on the optimal PID controller design confirm the superiority of AVURPSO algorithm to the optimization algorithms mentioned in this paper namely the VURPSO algorithm, the Ant Colony algorithm, and the conventional approach. Comparisons on the speed of convergence confirm that the proposed algorithm has a faster convergence in a less computation time to yield a global optimum value. The proposed AVURPSO can be used in the diverse areas of optimization problems such as industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning. The proposed AVURPSO algorithm is efficiently used to design an optimal PID controller.

  13. Local multiplicative Schwarz algorithms for convection-diffusion equations

    Science.gov (United States)

    Cai, Xiao-Chuan; Sarkis, Marcus

    1995-01-01

    We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

  14. Do convergent developmental mechanisms underlie convergent phenotypes?

    Science.gov (United States)

    Wray, Gregory A.

    2002-01-01

    Convergence is a pervasive evolutionary process, affecting many aspects of phenotype and even genotype. Relatively little is known about convergence in developmental processes, however, nor about the degree to which convergence in development underlies convergence in anatomy. A switch in the ecology of sea urchins from feeding to nonfeeding larvae illustrates how convergence in development can be associated with convergence in anatomy. Comparisons to more distantly related taxa, however, suggest that this association may be limited to relatively close phylogenetic comparisons. Similarities in gene expression during development provide another window into the association between convergence in developmental processes and convergence in anatomy. Several well-studied transcription factors exhibit likely cases of convergent gene expression in distantly related animal phyla. Convergence in regulatory gene expression domains is probably more common than generally acknowledged, and can arise for several different reasons. Copyright 2002 S. Karger AG, Basel.

  15. A chaos-based evolutionary algorithm for general nonlinear programming problems

    International Nuclear Information System (INIS)

    El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

    2016-01-01

    In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

  16. Structural hybrid reliability index and its convergent solving method based on random–fuzzy–interval reliability model

    Directory of Open Access Journals (Sweden)

    Hai An

    2016-08-01

    Full Text Available Aiming to resolve the problems of a variety of uncertainty variables that coexist in the engineering structure reliability analysis, a new hybrid reliability index to evaluate structural hybrid reliability, based on the random–fuzzy–interval model, is proposed in this article. The convergent solving method is also presented. First, the truncated probability reliability model, the fuzzy random reliability model, and the non-probabilistic interval reliability model are introduced. Then, the new hybrid reliability index definition is presented based on the random–fuzzy–interval model. Furthermore, the calculation flowchart of the hybrid reliability index is presented and it is solved using the modified limit-step length iterative algorithm, which ensures convergence. And the validity of convergent algorithm for the hybrid reliability model is verified through the calculation examples in literature. In the end, a numerical example is demonstrated to show that the hybrid reliability index is applicable for the wear reliability assessment of mechanisms, where truncated random variables, fuzzy random variables, and interval variables coexist. The demonstration also shows the good convergence of the iterative algorithm proposed in this article.

  17. Minimum Probability of Error-Based Equalization Algorithms for Fading Channels

    Directory of Open Access Journals (Sweden)

    Janos Levendovszky

    2007-06-01

    Full Text Available Novel channel equalizer algorithms are introduced for wireless communication systems to combat channel distortions resulting from multipath propagation. The novel algorithms are based on newly derived bounds on the probability of error (PE and guarantee better performance than the traditional zero forcing (ZF or minimum mean square error (MMSE algorithms. The new equalization methods require channel state information which is obtained by a fast adaptive channel identification algorithm. As a result, the combined convergence time needed for channel identification and PE minimization still remains smaller than the convergence time of traditional adaptive algorithms, yielding real-time equalization. The performance of the new algorithms is tested by extensive simulations on standard mobile channels.

  18. Recursive automatic classification algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Bauman, E V; Dorofeyuk, A A

    1982-03-01

    A variational statement of the automatic classification problem is given. The dependence of the form of the optimal partition surface on the form of the classification objective functional is investigated. A recursive algorithm is proposed for maximising a functional of reasonably general form. The convergence problem is analysed in connection with the proposed algorithm. 8 references.

  19. Modelling Embedded Systems by Non-Monotonic Refinement

    NARCIS (Netherlands)

    Mader, Angelika H.; Marincic, J.; Wupper, H.

    2008-01-01

    This paper addresses the process of modelling embedded sys- tems for formal verification. We propose a modelling process built on non-monotonic refinement and a number of guidelines. The outcome of the modelling process is a model, together with a correctness argument that justifies our modelling

  20. An analysis of the stability and monotonicity of a kind of control models

    Directory of Open Access Journals (Sweden)

    LU Yifa

    2013-06-01

    Full Text Available The stability and monotonicity of control systems with parameters are considered.By the iterative relationship of the coefficients of characteristic polynomials and the Mathematica software,some sufficient conditions for the monotonicity and stability of systems are given.

  1. Alternative solution algorithm for coupled thermal-hydraulic problems

    International Nuclear Information System (INIS)

    Farnsworth, D.A.; Rice, J.G.

    1986-01-01

    A thermal-hydraulic system involves flow of a fluid for which a combined solution of the continuity, momentum, and energy equations is required. When the solutions of the energy and momentum fields are dependent on each other, the system is said to be thermally coupled. A common problem encountered in the numerical solution of strongly coupled thermal-hydraulic problems is a very slow rate of convergence or a complete lack of convergence. Many times this degradation in convergence is due to the lack of true coupling between the energy and momentum fields during the iteration process. In the most widely used solution algorithms - such as the SIMPLE algorithm and its many variants - a sequential solution technique is required. That is, the solution process alternates between the flow and energy fields until a converged solution is obtained. This approach allows only implicit energy-momentum coupling. To improve the convergence rate for strongly coupled problems, a practical solution algorithm that can accommodate true energy-momentum coupling terms was developed. A complete simultaneous (versus sequential) solution of the governing conservation equations utilizing a line-by-line solution was developed and direct coupling terms between the momentum and energy fields were added utilizing a modified Newton-Raphson technique

  2. An Improved Routing Optimization Algorithm Based on Travelling Salesman Problem for Social Networks

    Directory of Open Access Journals (Sweden)

    Naixue Xiong

    2017-06-01

    Full Text Available A social network is a social structure, which is organized by the relationships or interactions between individuals or groups. Humans link the physical network with social network, and the services in the social world are based on data and analysis, which directly influence decision making in the physical network. In this paper, we focus on a routing optimization algorithm, which solves a well-known and popular problem. Ant colony algorithm is proposed to solve this problem effectively, but random selection strategy of the traditional algorithm causes evolution speed to be slow. Meanwhile, positive feedback and distributed computing model make the algorithm quickly converge. Therefore, how to improve convergence speed and search ability of algorithm is the focus of the current research. The paper proposes the improved scheme. Considering the difficulty about searching for next better city, new parameters are introduced to improve probability of selection, and delay convergence speed of algorithm. To avoid the shortest path being submerged, and improve sensitive speed of finding the shortest path, it updates pheromone regulation formula. The results show that the improved algorithm can effectively improve convergence speed and search ability for achieving higher accuracy and optimal results.

  3. Self-Adaptive Step Firefly Algorithm

    Directory of Open Access Journals (Sweden)

    Shuhao Yu

    2013-01-01

    Full Text Available In the standard firefly algorithm, each firefly has the same step settings and its values decrease from iteration to iteration. Therefore, it may fall into the local optimum. Furthermore, the decreasing of step is restrained by the maximum of iteration, which has an influence on the convergence speed and precision. In order to avoid falling into the local optimum and reduce the impact of the maximum of iteration, a self-adaptive step firefly algorithm is proposed in the paper. Its core idea is setting the step of each firefly varying with the iteration, according to each firefly’s historical information and current situation. Experiments are made to show the performance of our approach compared with the standard FA, based on sixteen standard testing benchmark functions. The results reveal that our method can prevent the premature convergence and improve the convergence speed and accurateness.

  4. Optimizing graph algorithms on pregel-like systems

    KAUST Repository

    Salihoglu, Semih; Widom, Jennifer

    2014-01-01

    We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high

  5. CFD simulation of simultaneous monotonic cooling and surface heat transfer coefficient

    International Nuclear Information System (INIS)

    Mihálka, Peter; Matiašovský, Peter

    2016-01-01

    The monotonic heating regime method for determination of thermal diffusivity is based on the analysis of an unsteady-state (stabilised) thermal process characterised by an independence of the space-time temperature distribution on initial conditions. At the first kind of the monotonic regime a sample of simple geometry is heated / cooled at constant ambient temperature. The determination of thermal diffusivity requires the determination rate of a temperature change and simultaneous determination of the first eigenvalue. According to a characteristic equation the first eigenvalue is a function of the Biot number defined by a surface heat transfer coefficient and thermal conductivity of an analysed material. Knowing the surface heat transfer coefficient and the first eigenvalue the thermal conductivity can be determined. The surface heat transport coefficient during the monotonic regime can be determined by the continuous measurement of long-wave radiation heat flow and the photoelectric measurement of the air refractive index gradient in a boundary layer. CFD simulation of the cooling process was carried out to analyse local convective and radiative heat transfer coefficients more in detail. Influence of ambient air flow was analysed. The obtained eigenvalues and corresponding surface heat transfer coefficient values enable to determine thermal conductivity of the analysed specimen together with its thermal diffusivity during a monotonic heating regime.

  6. A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution

    Directory of Open Access Journals (Sweden)

    Lijin Wang

    2015-01-01

    Full Text Available The backtracking search optimization algorithm (BSA is a new nature-inspired method which possesses a memory to take advantage of experiences gained from previous generation to guide the population to the global optimum. BSA is capable of solving multimodal problems, but it slowly converges and poorly exploits solution. The differential evolution (DE algorithm is a robust evolutionary algorithm and has a fast convergence speed in the case of exploitive mutation strategies that utilize the information of the best solution found so far. In this paper, we propose a hybrid backtracking search optimization algorithm with differential evolution, called HBD. In HBD, DE with exploitive strategy is used to accelerate the convergence by optimizing one worse individual according to its probability at each iteration process. A suit of 28 benchmark functions are employed to verify the performance of HBD, and the results show the improvement in effectiveness and efficiency of hybridization of BSA and DE.

  7. Application of Improved APO Algorithm in Vulnerability Assessment and Reconstruction of Microgrid

    Science.gov (United States)

    Xie, Jili; Ma, Hailing

    2018-01-01

    Artificial Physics Optimization (APO) has good global search ability and can avoid the premature convergence phenomenon in PSO algorithm, which has good stability of fast convergence and robustness. On the basis of APO of the vector model, a reactive power optimization algorithm based on improved APO algorithm is proposed for the static structure and dynamic operation characteristics of microgrid. The simulation test is carried out through the IEEE 30-bus system and the result shows that the algorithm has better efficiency and accuracy compared with other optimization algorithms.

  8. Modified Firefly Algorithm based controller design for integrating and unstable delay processes

    Directory of Open Access Journals (Sweden)

    A. Gupta

    2016-03-01

    Full Text Available In this paper, Modified Firefly Algorithm has been used for optimizing the controller parameters of Smith predictor structure. The proposed algorithm modifies the position formula of the standard Firefly Algorithm in order to achieve faster convergence rate. Performance criteria Integral Square Error (ISE is optimized using this optimization technique. Simulation results show high performance for Modified Firefly Algorithm as compared to conventional Firefly Algorithm in terms of convergence rate. Integrating and unstable delay processes are taken as examples to indicate the performance of the proposed method.

  9. Semi-convergence and relaxation parameters for a class of SIRT algorithms

    DEFF Research Database (Denmark)

    Elfving, Tommy; Nikazad, Touraj; Hansen, Per Christian

    2010-01-01

    This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters...

  10. MM Algorithms for Geometric and Signomial Programming.

    Science.gov (United States)

    Lange, Kenneth; Zhou, Hua

    2014-02-01

    This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

  11. Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation

    Directory of Open Access Journals (Sweden)

    Namyong Kim

    2016-06-01

    Full Text Available The minimum error entropy (MEE algorithm is known to be superior in signal processing applications under impulsive noise. In this paper, based on the analysis of behavior of the optimum weight and the properties of robustness against impulsive noise, a normalized version of the MEE algorithm is proposed. The step size of the MEE algorithm is normalized with the power of input entropy that is estimated recursively for reducing its computational complexity. The proposed algorithm yields lower minimum MSE (mean squared error and faster convergence speed simultaneously than the original MEE algorithm does in the equalization simulation. On the condition of the same convergence speed, its performance enhancement in steady state MSE is above 3 dB.

  12. Improved multivariate polynomial factoring algorithm

    International Nuclear Information System (INIS)

    Wang, P.S.

    1978-01-01

    A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known problems of the original algorithm, namely, the leading coefficient problem, the bad-zero problem and the occurrence of extraneous factors. It has an algorithm for correctly predetermining leading coefficients of the factors. A new and efficient p-adic algorithm named EEZ is described. Bascially it is a linearly convergent variable-by-variable parallel construction. The improved algorithm is generally faster and requires less store then the original algorithm. Machine examples with comparative timing are included

  13. Evaluation of the Monotonic Lagrangian Grid and Lat-Long Grid for Air Traffic Management

    Science.gov (United States)

    Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay

    2011-01-01

    The Air Traffic Monotonic Lagrangian Grid (ATMLG) is used to simulate a 24 hour period of air traffic flow in the National Airspace System (NAS). During this time period, there are 41,594 flights over the United States, and the flight plan information (departure and arrival airports and times, and waypoints along the way) are obtained from an Federal Aviation Administration (FAA) Enhanced Traffic Management System (ETMS) dataset. Two simulation procedures are tested and compared: one based on the Monotonic Lagrangian Grid (MLG), and the other based on the stationary Latitude-Longitude (Lat- Long) grid. Simulating one full day of air traffic over the United States required the following amounts of CPU time on a single processor of an SGI Altix: 88 s for the MLG method, and 163 s for the Lat-Long grid method. We present a discussion of the amount of CPU time required for each of the simulation processes (updating aircraft trajectories, sorting, conflict detection and resolution, etc.), and show that the main advantage of the MLG method is that it is a general sorting algorithm that can sort on multiple properties. We discuss how many MLG neighbors must be considered in the separation assurance procedure in order to ensure a five-mile separation buffer between aircraft, and we investigate the effect of removing waypoints from aircraft trajectories. When aircraft choose their own trajectory, there are more flights with shorter duration times and fewer CD&R maneuvers, resulting in significant fuel savings.

  14. RES: Regularized Stochastic BFGS Algorithm

    Science.gov (United States)

    Mokhtari, Aryan; Ribeiro, Alejandro

    2014-12-01

    RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

  15. An Examination of Cooper's Test for Monotonic Trend

    Science.gov (United States)

    Hsu, Louis

    1977-01-01

    A statistic for testing monotonic trend that has been presented in the literature is shown not to be the binomial random variable it is contended to be, but rather it is linearly related to Kendall's tau statistic. (JKS)

  16. Service Composition Instantiation Based on Cross-Modified Artificial Bee Colony Algorithm

    Institute of Scientific and Technical Information of China (English)

    Lei Huo; Zhiliang Wang

    2016-01-01

    Internet of things (IoT) imposes new challenges on service composition as it is difficult to manage a quick instantiation of a complex services from a growing number of dynamic candidate services.A cross-modified Artificial Bee Colony Algorithm (CMABC) is proposed to achieve the optimal solution services in an acceptable time and high accuracy.Firstly,web service instantiation model was established.What is more,to overcome the problem of discrete and chaotic solution space,the global optimal solution was used to accelerate convergence rate by imitating the cross operation of Genetic algorithm (GA).The simulation experiment result shows that CMABC exhibited faster convergence speed and better convergence accuracy than some other intelligent optimization algorithms.

  17. Resizing Technique-Based Hybrid Genetic Algorithm for Optimal Drift Design of Multistory Steel Frame Buildings

    Directory of Open Access Journals (Sweden)

    Hyo Seon Park

    2014-01-01

    Full Text Available Since genetic algorithm-based optimization methods are computationally expensive for practical use in the field of structural optimization, a resizing technique-based hybrid genetic algorithm for the drift design of multistory steel frame buildings is proposed to increase the convergence speed of genetic algorithms. To reduce the number of structural analyses required for the convergence, a genetic algorithm is combined with a resizing technique that is an efficient optimal technique to control the drift of buildings without the repetitive structural analysis. The resizing technique-based hybrid genetic algorithm proposed in this paper is applied to the minimum weight design of three steel frame buildings. To evaluate the performance of the algorithm, optimum weights, computational times, and generation numbers from the proposed algorithm are compared with those from a genetic algorithm. Based on the comparisons, it is concluded that the hybrid genetic algorithm shows clear improvements in convergence properties.

  18. Field-Split Preconditioned Inexact Newton Algorithms

    KAUST Repository

    Liu, Lulu

    2015-06-02

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

  19. Field-Split Preconditioned Inexact Newton Algorithms

    KAUST Repository

    Liu, Lulu; Keyes, David E.

    2015-01-01

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

  20. Dimension elevation in Müntz spaces: A new emergence of the Müntz condition

    KAUST Repository

    Ait-Haddou, Rachid

    2014-05-01

    We show that the limiting polygon generated by the dimension elevation algorithm with respect to the Müntz space span(1,tr1,tr2,trm,. . .), with 0 < r1 < r2 < ⋯ < r m < ⋯ and lim n →∞r n = ∞, over an interval [a, b] ⊂ ] 0, ∞ [ converges to the underlying Chebyshev-Bézier curve if and only if the Müntz condition ∑i=1∞1ri=∞ is satisfied. The surprising emergence of the Müntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms. The question of convergence with no condition of monotonicity or positivity on the pairwise distinct real numbers r i remains an open problem. © 2014 Elsevier Inc.

  1. Multicloud: Multigrid convergence with a meshless operator

    International Nuclear Information System (INIS)

    Katz, Aaron; Jameson, Antony

    2009-01-01

    The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.

  2. Solving symmetric-definite quadratic lambda-matrix problems without factorization

    International Nuclear Information System (INIS)

    Scott, D.S.; Ward, R.C.

    1982-01-01

    Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

  3. Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

    International Nuclear Information System (INIS)

    Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

    2005-01-01

    Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

  4. L∞-error estimate for a system of elliptic quasivariational inequalities

    Directory of Open Access Journals (Sweden)

    M. Boulbrachene

    2003-01-01

    Full Text Available We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs. Under W2,p(Ω-regularity of the continuous solution, a quasi-optimal L∞-convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs.

  5. ENHANCED HYBRID PSO – ACO ALGORITHM FOR GRID SCHEDULING

    Directory of Open Access Journals (Sweden)

    P. Mathiyalagan

    2010-07-01

    Full Text Available Grid computing is a high performance computing environment to solve larger scale computational demands. Grid computing contains resource management, task scheduling, security problems, information management and so on. Task scheduling is a fundamental issue in achieving high performance in grid computing systems. A computational GRID is typically heterogeneous in the sense that it combines clusters of varying sizes, and different clusters typically contains processing elements with different level of performance. In this, heuristic approaches based on particle swarm optimization and ant colony optimization algorithms are adopted for solving task scheduling problems in grid environment. Particle Swarm Optimization (PSO is one of the latest evolutionary optimization techniques by nature. It has the better ability of global searching and has been successfully applied to many areas such as, neural network training etc. Due to the linear decreasing of inertia weight in PSO the convergence rate becomes faster, which leads to the minimal makespan time when used for scheduling. To make the convergence rate faster, the PSO algorithm is improved by modifying the inertia parameter, such that it produces better performance and gives an optimized result. The ACO algorithm is improved by modifying the pheromone updating rule. ACO algorithm is hybridized with PSO algorithm for efficient result and better convergence in PSO algorithm.

  6. SUPER-SAPSO: A New SA-Based PSO Algorithm

    NARCIS (Netherlands)

    Bahrepour, M.; Mahdipour, E.; Cheloi, R.; Yaghoobi, M.

    2008-01-01

    Swarm Optimisation (PSO) has been received increasing attention due to its simplicity and reasonable convergence speed surpassing genetic algorithm in some circumstances. In order to improve convergence speed or to augment the exploration area within the solution space to find a better optimum

  7. A Novel Evolutionary Algorithm Inspired by Beans Dispersal

    Directory of Open Access Journals (Sweden)

    Xiaoming Zhang

    2013-02-01

    Full Text Available Inspired by the transmission of beans in nature, a novel evolutionary algorithm-Bean Optimization Algorithm (BOA is proposed in this paper. BOA is mainly based on the normal distribution which is an important continuous probability distribution of quantitative phenomena. Through simulating the self-adaptive phenomena of plant, BOA is designed for solving continuous optimization problems. We also analyze the global convergence of BOA by using the Solis and Wetsarsquo; research results. The conclusion is that BOA can converge to the global optimization solution with probability one. In order to validate its effectiveness, BOA is tested against benchmark functions. And its performance is also compared with that of particle swarm optimization (PSO algorithm. The experimental results show that BOA has competitive performance to PSO in terms of accuracy and convergence speed on the explored tests and stands out as a promising alternative to existing optimization methods for engineering designs or applications.

  8. Improved ultrashort pulse-retrieval algorithm for frequency-resolved optical gating

    International Nuclear Information System (INIS)

    DeLong, K.W.; Trebino, R.

    1994-01-01

    We report on significant improvements in the pulse-retrieval algorithm used to reconstruct the amplitude and the phase of ultrashort optical pulses from the experimental frequency-resolved optical gating trace data in the polarization-gate geometry. These improvements involve the use of an intensity constraint, an overcorrection technique, and a multidimensional minimization scheme. While the previously published, basic algorithm converged for most common ultrashort pulses, it failed to retrieve pulses with significant intensity substructure. The improved composite algorithm successfully converges for such pulses. It can now retrieve essentially all pulses of practical interest. We present examples of complex waveforms that were retrieved by the improved algorithm

  9. Theory of affine projection algorithms for adaptive filtering

    CERN Document Server

    Ozeki, Kazuhiko

    2016-01-01

    This book focuses on theoretical aspects of the affine projection algorithm (APA) for adaptive filtering. The APA is a natural generalization of the classical, normalized least-mean-squares (NLMS) algorithm. The book first explains how the APA evolved from the NLMS algorithm, where an affine projection view is emphasized. By looking at those adaptation algorithms from such a geometrical point of view, we can find many of the important properties of the APA, e.g., the improvement of the convergence rate over the NLMS algorithm especially for correlated input signals. After the birth of the APA in the mid-1980s, similar algorithms were put forward by other researchers independently from different perspectives. This book shows that they are variants of the APA, forming a family of APAs. Then it surveys research on the convergence behavior of the APA, where statistical analyses play important roles. It also reviews developments of techniques to reduce the computational complexity of the APA, which are important f...

  10. Convergence of Algorithms for Reconstructing Convex Bodies and Directional Measures

    DEFF Research Database (Denmark)

    Gardner, Richard; Kiderlen, Markus; Milanfar, Peyman

    2006-01-01

    We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best...

  11. A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

    Science.gov (United States)

    Madyastha, Raghavendra K.; Aazhang, Behnaam; Henson, Troy F.; Huxhold, Wendy L.

    1992-01-01

    This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

  12. Rational functions with maximal radius of absolute monotonicity

    KAUST Repository

    Loczi, Lajos; Ketcheson, David I.

    2014-01-01

    -Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend

  13. A note on monotone real circuits

    Czech Academy of Sciences Publication Activity Database

    Hrubeš, Pavel; Pudlák, Pavel

    2018-01-01

    Roč. 131, March (2018), s. 15-19 ISSN 0020-0190 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : computational complexity * monotone real circuit * Karchmer-Wigderson game Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.748, year: 2016 http ://www.sciencedirect.com/science/article/pii/S0020019017301965?via%3Dihub

  14. A note on monotone real circuits

    Czech Academy of Sciences Publication Activity Database

    Hrubeš, Pavel; Pudlák, Pavel

    2018-01-01

    Roč. 131, March (2018), s. 15-19 ISSN 0020-0190 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : computational complexity * monotone real circuit * Karchmer-Wigderson game Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.748, year: 2016 http://www.sciencedirect.com/science/article/pii/S0020019017301965?via%3Dihub

  15. Interval Routing and Minor-Monotone Graph Parameters

    NARCIS (Netherlands)

    Bakker, E.M.; Bodlaender, H.L.; Tan, R.B.; Leeuwen, J. van

    2006-01-01

    We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdi`ere’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the

  16. A Hybrid Approach to Proving Memory Reference Monotonicity

    KAUST Repository

    Oancea, Cosmin E.

    2013-01-01

    Array references indexed by non-linear expressions or subscript arrays represent a major obstacle to compiler analysis and to automatic parallelization. Most previous proposed solutions either enhance the static analysis repertoire to recognize more patterns, to infer array-value properties, and to refine the mathematical support, or apply expensive run time analysis of memory reference traces to disambiguate these accesses. This paper presents an automated solution based on static construction of access summaries, in which the reference non-linearity problem can be solved for a large number of reference patterns by extracting arbitrarily-shaped predicates that can (in)validate the reference monotonicity property and thus (dis)prove loop independence. Experiments on six benchmarks show that our general technique for dynamic validation of the monotonicity property can cover a large class of codes, incurs minimal run-time overhead and obtains good speedups. © 2013 Springer-Verlag.

  17. An improved version of Inverse Distance Weighting metamodel assisted Harmony Search algorithm for truss design optimization

    Directory of Open Access Journals (Sweden)

    Y. Gholipour

    Full Text Available This paper focuses on a metamodel-based design optimization algorithm. The intention is to improve its computational cost and convergence rate. Metamodel-based optimization method introduced here, provides the necessary means to reduce the computational cost and convergence rate of the optimization through a surrogate. This algorithm is a combination of a high quality approximation technique called Inverse Distance Weighting and a meta-heuristic algorithm called Harmony Search. The outcome is then polished by a semi-tabu search algorithm. This algorithm adopts a filtering system and determines solution vectors where exact simulation should be applied. The performance of the algorithm is evaluated by standard truss design problems and there has been a significant decrease in the computational effort and improvement of convergence rate.

  18. Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

    KAUST Repository

    Mozartova, A.; Savostianov, I.; Hundsdorfer, W.

    2015-01-01

    © 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.

  19. Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

    KAUST Repository

    Mozartova, A.

    2015-05-01

    © 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.

  20. The regularized monotonicity method: detecting irregular indefinite inclusions

    DEFF Research Database (Denmark)

    Garde, Henrik; Staboulis, Stratos

    2018-01-01

    inclusions, where the conductivity distribution has both more and less conductive parts relative to the background conductivity; one such method is the monotonicity method of Harrach, Seo, and Ullrich. We formulate the method for irregular indefinite inclusions, meaning that we make no regularity assumptions...

  1. A note on monotonicity of item response functions for ordered polytomous item response theory models.

    Science.gov (United States)

    Kang, Hyeon-Ah; Su, Ya-Hui; Chang, Hua-Hua

    2018-03-08

    A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models. Five models that are widely used in operational assessments are considered for proof: the generalized partial credit model (Muraki, 1992, Applied Psychological Measurement, 16, 159), the nominal model (Bock, 1972, Psychometrika, 37, 29), the partial credit model (Masters, 1982, Psychometrika, 47, 147), the rating scale model (Andrich, 1978, Psychometrika, 43, 561), and the graded response model (Samejima, 1972, A general model for free-response data (Psychometric Monograph no. 18). Psychometric Society, Richmond). The study asserts that the item response functions in these models strictly increase in θ and thus there exists strict monotonicity between τ and θ under certain specified conditions. This conclusion validates the practice of customarily using τ in place of θ in applied settings and provides theoretical grounds for one-to-one transformations between the two scales. © 2018 The British Psychological Society.

  2. Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

    Directory of Open Access Journals (Sweden)

    Mervan Pašić

    2016-10-01

    Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

  3. Robust sampling-sourced numerical retrieval algorithm for optical energy loss function based on log–log mesh optimization and local monotonicity preserving Steffen spline

    Energy Technology Data Exchange (ETDEWEB)

    Maglevanny, I.I., E-mail: sianko@list.ru [Volgograd State Social Pedagogical University, 27 Lenin Avenue, Volgograd 400131 (Russian Federation); Smolar, V.A. [Volgograd State Technical University, 28 Lenin Avenue, Volgograd 400131 (Russian Federation)

    2016-01-15

    We introduce a new technique of interpolation of the energy-loss function (ELF) in solids sampled by empirical optical spectra. Finding appropriate interpolation methods for ELFs poses several challenges. The sampled ELFs are usually very heterogeneous, can originate from various sources thus so called “data gaps” can appear, and significant discontinuities and multiple high outliers can be present. As a result an interpolation based on those data may not perform well at predicting reasonable physical results. Reliable interpolation tools, suitable for ELF applications, should therefore satisfy several important demands: accuracy and predictive power, robustness and computational efficiency, and ease of use. We examined the effect on the fitting quality due to different interpolation schemes with emphasis on ELF mesh optimization procedures and we argue that the optimal fitting should be based on preliminary log–log scaling data transforms by which the non-uniformity of sampled data distribution may be considerably reduced. The transformed data are then interpolated by local monotonicity preserving Steffen spline. The result is a piece-wise smooth fitting curve with continuous first-order derivatives that passes through all data points without spurious oscillations. Local extrema can occur only at grid points where they are given by the data, but not in between two adjacent grid points. It is found that proposed technique gives the most accurate results and also that its computational time is short. Thus, it is feasible using this simple method to address practical problems associated with interaction between a bulk material and a moving electron. A compact C++ implementation of our algorithm is also presented.

  4. Robust sampling-sourced numerical retrieval algorithm for optical energy loss function based on log–log mesh optimization and local monotonicity preserving Steffen spline

    International Nuclear Information System (INIS)

    Maglevanny, I.I.; Smolar, V.A.

    2016-01-01

    We introduce a new technique of interpolation of the energy-loss function (ELF) in solids sampled by empirical optical spectra. Finding appropriate interpolation methods for ELFs poses several challenges. The sampled ELFs are usually very heterogeneous, can originate from various sources thus so called “data gaps” can appear, and significant discontinuities and multiple high outliers can be present. As a result an interpolation based on those data may not perform well at predicting reasonable physical results. Reliable interpolation tools, suitable for ELF applications, should therefore satisfy several important demands: accuracy and predictive power, robustness and computational efficiency, and ease of use. We examined the effect on the fitting quality due to different interpolation schemes with emphasis on ELF mesh optimization procedures and we argue that the optimal fitting should be based on preliminary log–log scaling data transforms by which the non-uniformity of sampled data distribution may be considerably reduced. The transformed data are then interpolated by local monotonicity preserving Steffen spline. The result is a piece-wise smooth fitting curve with continuous first-order derivatives that passes through all data points without spurious oscillations. Local extrema can occur only at grid points where they are given by the data, but not in between two adjacent grid points. It is found that proposed technique gives the most accurate results and also that its computational time is short. Thus, it is feasible using this simple method to address practical problems associated with interaction between a bulk material and a moving electron. A compact C++ implementation of our algorithm is also presented.

  5. The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects

    NARCIS (Netherlands)

    Tijs, S.H.; Moretti, S.; Brânzei, R.; Norde, H.W.

    2005-01-01

    A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems

  6. Rational functions with maximal radius of absolute monotonicity

    KAUST Repository

    Loczi, Lajos

    2014-05-19

    We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parameter families of rational functions. Moreover, we prove earlier conjectured optimal radii in some families with 2 or 3 parameters via uniqueness arguments for systems of polynomial inequalities. Our results also prove the optimality of some strong stability preserving implicit and singly diagonally implicit Runge-Kutta methods. Whereas previous results in this area were primarily numerical, we give all constants as exact algebraic numbers.

  7. Approximated affine projection algorithm for feedback cancellation in hearing aids.

    Science.gov (United States)

    Lee, Sangmin; Kim, In-Young; Park, Young-Cheol

    2007-09-01

    We propose an approximated affine projection (AP) algorithm for feedback cancellation in hearing aids. It is based on the conventional approach using the Gauss-Seidel (GS) iteration, but provides more stable convergence behaviour even with small step sizes. In the proposed algorithm, a residue of the weighted error vector, instead of the current error sample, is used to provide stable convergence. A new learning rate control scheme is also applied to the proposed algorithm to prevent signal cancellation and system instability. The new scheme determines step size in proportion to the prediction factor of the input, so that adaptation is inhibited whenever tone-like signals are present in the input. Simulation results verified the efficiency of the proposed algorithm.

  8. Exponentially-convergent Monte Carlo for the 1-D transport equation

    International Nuclear Information System (INIS)

    Peterson, J. R.; Morel, J. E.; Ragusa, J. C.

    2013-01-01

    We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)

  9. A Dynamic Multistage Hybrid Swarm Intelligence Optimization Algorithm for Function Optimization

    Directory of Open Access Journals (Sweden)

    Daqing Wu

    2012-01-01

    Full Text Available A novel dynamic multistage hybrid swarm intelligence optimization algorithm is introduced, which is abbreviated as DM-PSO-ABC. The DM-PSO-ABC combined the exploration capabilities of the dynamic multiswarm particle swarm optimizer (PSO and the stochastic exploitation of the cooperative artificial bee colony algorithm (CABC for solving the function optimization. In the proposed hybrid algorithm, the whole process is divided into three stages. In the first stage, a dynamic multiswarm PSO is constructed to maintain the population diversity. In the second stage, the parallel, positive feedback of CABC was implemented in each small swarm. In the third stage, we make use of the particle swarm optimization global model, which has a faster convergence speed to enhance the global convergence in solving the whole problem. To verify the effectiveness and efficiency of the proposed hybrid algorithm, various scale benchmark problems are tested to demonstrate the potential of the proposed multistage hybrid swarm intelligence optimization algorithm. The results show that DM-PSO-ABC is better in the search precision, and convergence property and has strong ability to escape from the local suboptima when compared with several other peer algorithms.

  10. Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings

    Directory of Open Access Journals (Sweden)

    Bin-Chao Deng

    2013-01-01

    Full Text Available Let H be a real Hilbert space. Let T1,T2:H→H be k1-, k2-strictly pseudononspreading mappings; let αn and βn be two real sequences in (0,1. For given x0∈H, the sequence xn is generated iteratively by xn+1=βnxn+1-βnTw1αnγfxn+I-μαnBTw2xn, ∀n∈N, where Twi=1−wiI+wiTi with i=1,2 and B:H→H is strongly monotone and Lipschitzian. Under some mild conditions on parameters αn and βn, we prove that the sequence xn converges strongly to the set FixT1∩FixT2 of fixed points of a pair of strictly pseudononspreading mappings T1 and T2.

  11. Similarity-First Search: a new algorithm with application to Robinsonian matrix recognition

    NARCIS (Netherlands)

    M. Laurent (Monique); M. Seminaroti (Matteo)

    2016-01-01

    textabstractWe present a new efficient combinatorial algorithm for recognizing if a given symmetric matrix is Robinsonian, i.e., if its rows and columns can be simultaneously reordered so that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. As main ingredient

  12. Similarity-first search : A new algorithm with application to Robinsonian matrix recognition

    NARCIS (Netherlands)

    Laurent, Monique; Seminaroti, Matteo

    2017-01-01

    We present a new efficient combinatorial algorithm for recognizing if a given symmetric matrix is Robinsonian, i.e., if its rows and columns can be simultaneously reordered so that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. As the main ingredient we

  13. Thermal effects on the enhanced ductility in non-monotonic uniaxial tension of DP780 steel sheet

    Science.gov (United States)

    Majidi, Omid; Barlat, Frederic; Korkolis, Yannis P.; Fu, Jiawei; Lee, Myoung-Gyu

    2016-11-01

    To understand the material behavior during non-monotonic loading, uniaxial tension tests were conducted in three modes, namely, the monotonic loading, loading with periodic relaxation and periodic loading-unloadingreloading, at different strain rates (0.001/s to 0.01/s). In this study, the temperature gradient developing during each test and its contribution to increasing the apparent ductility of DP780 steel sheets were considered. In order to assess the influence of temperature, isothermal uniaxial tension tests were also performed at three temperatures (298 K, 313 K and 328 K (25 °C, 40 °C and 55 °C)). A digital image correlation system coupled with an infrared thermography was used in the experiments. The results show that the non-monotonic loading modes increased the apparent ductility of the specimens. It was observed that compared with the monotonic loading, the temperature gradient became more uniform when a non-monotonic loading was applied.

  14. On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

    Science.gov (United States)

    Korda, Milan; Mezić, Igor

    2018-04-01

    Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307-1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by sampling at M points in the state space. Assuming that the samples are drawn either independently or ergodically from some measure μ , it was shown in Klus et al. (J Comput Dyn 3(1):51-79, 2016) that, in the limit as M→ ∞, the EDMD operator K_{N,M} converges to K_N, where K_N is the L_2(μ )-orthogonal projection of the action of the Koopman operator on the finite-dimensional subspace of observables. We show that, as N → ∞, the operator K_N converges in the strong operator topology to the Koopman operator. This in particular implies convergence of the predictions of future values of a given observable over any finite time horizon, a fact important for practical applications such as forecasting, estimation and control. In addition, we show that accumulation points of the spectra of K_N correspond to the eigenvalues of the Koopman operator with the associated eigenfunctions converging weakly to an eigenfunction of the Koopman operator, provided that the weak limit of the eigenfunctions is nonzero. As a by-product, we propose an analytic version of the EDMD algorithm which, under some assumptions, allows one to construct K_N directly, without the use of sampling. Finally, under additional assumptions, we analyze convergence of K_{N,N} (i.e., M=N), proving convergence, along a subsequence, to weak eigenfunctions (or eigendistributions) related to the eigenmeasures of the Perron-Frobenius operator. No assumptions on the observables belonging to a finite-dimensional invariant subspace of the Koopman operator are required throughout.

  15. Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis.

    Science.gov (United States)

    Bornkamp, Björn; Ickstadt, Katja

    2009-03-01

    In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose-response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose-response analysis.

  16. Newton algorithm for Hamiltonian characterization in quantum control

    International Nuclear Information System (INIS)

    Ndong, M; Sugny, D; Salomon, J

    2014-01-01

    We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank–Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution. (paper)

  17. Quorum-Sensing Synchronization of Synthetic Toggle Switches: A Design Based on Monotone Dynamical Systems Theory.

    Directory of Open Access Journals (Sweden)

    Evgeni V Nikolaev

    2016-04-01

    Full Text Available Synthetic constructs in biotechnology, biocomputing, and modern gene therapy interventions are often based on plasmids or transfected circuits which implement some form of "on-off" switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens, and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular ("intrinsic" or environmental ("extrinsic" noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a "majority-vote" correction circuit, which brings deviant cells back into the required state, is highly desirable, and quorum-sensing has been suggested as a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. In this paper, we propose what we believe is the first such a design that has mathematically guaranteed properties of stability and auto-correction under certain conditions. Our approach is guided by concepts and theory from the field of "monotone" dynamical systems developed by M. Hirsch, H. Smith, and others. We benchmark our design by comparing it to an existing design which has been the subject of experimental and theoretical studies, illustrating its superiority in stability and self-correction of synchronization errors. Our stability analysis, based on dynamical systems theory, guarantees global convergence to steady states, ruling out unpredictable ("chaotic" behaviors and even sustained oscillations in the limit of convergence. These results are valid no matter what are the values of parameters, and are based only on the wiring diagram. The theory is complemented by extensive computational bifurcation analysis

  18. A novel algorithm of artificial immune system for high-dimensional function numerical optimization

    Institute of Scientific and Technical Information of China (English)

    DU Haifeng; GONG Maoguo; JIAO Licheng; LIU Ruochen

    2005-01-01

    Based on the clonal selection theory and immune memory theory, a novel artificial immune system algorithm, immune memory clonal programming algorithm (IMCPA), is put forward. Using the theorem of Markov chain, it is proved that IMCPA is convergent. Compared with some other evolutionary programming algorithms (like Breeder genetic algorithm), IMCPA is shown to be an evolutionary strategy capable of solving complex machine learning tasks, like high-dimensional function optimization, which maintains the diversity of the population and avoids prematurity to some extent, and has a higher convergence speed.

  19. Reduction theorems for weighted integral inequalities on the cone of monotone functions

    International Nuclear Information System (INIS)

    Gogatishvili, A; Stepanov, V D

    2013-01-01

    This paper surveys results related to the reduction of integral inequalities involving positive operators in weighted Lebesgue spaces on the real semi-axis and valid on the cone of monotone functions, to certain more easily manageable inequalities valid on the cone of non-negative functions. The case of monotone operators is new. As an application, a complete characterization for all possible integrability parameters is obtained for a number of Volterra operators. Bibliography: 118 titles

  20. Experiments with conjugate gradient algorithms for homotopy curve tracking

    Science.gov (United States)

    Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

    1991-01-01

    There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

  1. Bouc–Wen hysteresis model identification using Modified Firefly Algorithm

    International Nuclear Information System (INIS)

    Zaman, Mohammad Asif; Sikder, Urmita

    2015-01-01

    The parameters of Bouc–Wen hysteresis model are identified using a Modified Firefly Algorithm. The proposed algorithm uses dynamic process control parameters to improve its performance. The algorithm is used to find the model parameter values that results in the least amount of error between a set of given data points and points obtained from the Bouc–Wen model. The performance of the algorithm is compared with the performance of conventional Firefly Algorithm, Genetic Algorithm and Differential Evolution algorithm in terms of convergence rate and accuracy. Compared to the other three optimization algorithms, the proposed algorithm is found to have good convergence rate with high degree of accuracy in identifying Bouc–Wen model parameters. Finally, the proposed method is used to find the Bouc–Wen model parameters from experimental data. The obtained model is found to be in good agreement with measured data. - Highlights: • We describe a new method to find the Bouc–Wen hysteresis model parameters. • We propose a Modified Firefly Algorithm. • We compare our method with existing methods to find that the proposed method performs better. • We use our model to fit experimental results. Good agreement is found

  2. Bouc–Wen hysteresis model identification using Modified Firefly Algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Zaman, Mohammad Asif, E-mail: zaman@stanford.edu [Department of Electrical Engineering, Stanford University (United States); Sikder, Urmita [Department of Electrical Engineering and Computer Sciences, University of California, Berkeley (United States)

    2015-12-01

    The parameters of Bouc–Wen hysteresis model are identified using a Modified Firefly Algorithm. The proposed algorithm uses dynamic process control parameters to improve its performance. The algorithm is used to find the model parameter values that results in the least amount of error between a set of given data points and points obtained from the Bouc–Wen model. The performance of the algorithm is compared with the performance of conventional Firefly Algorithm, Genetic Algorithm and Differential Evolution algorithm in terms of convergence rate and accuracy. Compared to the other three optimization algorithms, the proposed algorithm is found to have good convergence rate with high degree of accuracy in identifying Bouc–Wen model parameters. Finally, the proposed method is used to find the Bouc–Wen model parameters from experimental data. The obtained model is found to be in good agreement with measured data. - Highlights: • We describe a new method to find the Bouc–Wen hysteresis model parameters. • We propose a Modified Firefly Algorithm. • We compare our method with existing methods to find that the proposed method performs better. • We use our model to fit experimental results. Good agreement is found.

  3. Partial coherence with application to the monotonicity problem of coherence involving skew information

    Science.gov (United States)

    Luo, Shunlong; Sun, Yuan

    2017-08-01

    Quantifications of coherence are intensively studied in the context of completely decoherent operations (i.e., von Neuamnn measurements, or equivalently, orthonormal bases) in recent years. Here we investigate partial coherence (i.e., coherence in the context of partially decoherent operations such as Lüders measurements). A bona fide measure of partial coherence is introduced. As an application, we address the monotonicity problem of K -coherence (a quantifier for coherence in terms of Wigner-Yanase skew information) [Girolami, Phys. Rev. Lett. 113, 170401 (2014), 10.1103/PhysRevLett.113.170401], which is introduced to realize a measure of coherence as axiomatized by Baumgratz, Cramer, and Plenio [Phys. Rev. Lett. 113, 140401 (2014), 10.1103/PhysRevLett.113.140401]. Since K -coherence fails to meet the necessary requirement of monotonicity under incoherent operations, it is desirable to remedy this monotonicity problem. We show that if we modify the original measure by taking skew information with respect to the spectral decomposition of an observable, rather than the observable itself, as a measure of coherence, then the problem disappears, and the resultant coherence measure satisfies the monotonicity. Some concrete examples are discussed and related open issues are indicated.

  4. Modern algorithms for large sparse eigenvalue problems

    International Nuclear Information System (INIS)

    Meyer, A.

    1987-01-01

    The volume is written for mathematicians interested in (numerical) linear algebra and in the solution of large sparse eigenvalue problems, as well as for specialists in engineering, who use the considered algorithms in the investigation of eigenoscillations of structures, in reactor physics, etc. Some variants of the algorithms based on the idea of a gradient-type direction of movement are presented and their convergence properties are discussed. From this, a general strategy for the direct use of preconditionings for the eigenvalue problem is derived. In this new approach the necessity of the solution of large linear systems is entirely avoided. Hence, these methods represent a new alternative to some other modern eigenvalue algorithms, as they show a slightly slower convergence on the one hand but essentially lower numerical and data processing problems on the other hand. A brief description and comparison of some well-known methods (i.e. simultaneous iteration, Lanczos algorithm) completes this volume. (author)

  5. Error Bounds for Augmented Truncations of Discrete-Time Block-Monotone Markov Chains under Geometric Drift Conditions

    OpenAIRE

    Masuyama, Hiroyuki

    2014-01-01

    In this paper we study the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distance between the stationary distributions of an original Markov chain and its augmented truncation. We also obtain such error bounds for more general cases, where an original Markov chain itself is not necessarily block monotone but is blockwise dominated by a block-monotone Markov chain. Finally,...

  6. Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces

    Directory of Open Access Journals (Sweden)

    Kalabušić S

    2009-01-01

    Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.

  7. Real-Coded Quantum-Inspired Genetic Algorithm-Based BP Neural Network Algorithm

    Directory of Open Access Journals (Sweden)

    Jianyong Liu

    2015-01-01

    Full Text Available The method that the real-coded quantum-inspired genetic algorithm (RQGA used to optimize the weights and threshold of BP neural network is proposed to overcome the defect that the gradient descent method makes the algorithm easily fall into local optimal value in the learning process. Quantum genetic algorithm (QGA is with good directional global optimization ability, but the conventional QGA is based on binary coding; the speed of calculation is reduced by the coding and decoding processes. So, RQGA is introduced to explore the search space, and the improved varied learning rate is adopted to train the BP neural network. Simulation test shows that the proposed algorithm is effective to rapidly converge to the solution conformed to constraint conditions.

  8. Similarity-First Search : A New Algorithm With Application to Robinsonian Matrix Recognition

    NARCIS (Netherlands)

    Laurent, Monique; Seminaroti, Matteo

    We present a new ecient combinatorial algorithm for recognizing if a given symmetric matrix is Robinsonian, i.e., if its rows and columns can be simultane- ously reordered so that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. As main ingredient we introduce

  9. A Fast Alternating Minimization Algorithm for Nonlocal Vectorial Total Variational Multichannel Image Denoising

    Directory of Open Access Journals (Sweden)

    Rubing Xi

    2014-01-01

    Full Text Available The variational models with nonlocal regularization offer superior image restoration quality over traditional method. But the processing speed remains a bottleneck due to the calculation quantity brought by the recent iterative algorithms. In this paper, a fast algorithm is proposed to restore the multichannel image in the presence of additive Gaussian noise by minimizing an energy function consisting of an l2-norm fidelity term and a nonlocal vectorial total variational regularization term. This algorithm is based on the variable splitting and penalty techniques in optimization. Following our previous work on the proof of the existence and the uniqueness of the solution of the model, we establish and prove the convergence properties of this algorithm, which are the finite convergence for some variables and the q-linear convergence for the rest. Experiments show that this model has a fabulous texture-preserving property in restoring color images. Both the theoretical derivation of the computation complexity analysis and the experimental results show that the proposed algorithm performs favorably in comparison to the widely used fixed point algorithm.

  10. Modified automatic term selection v2: A faster algorithm to calculate inelastic scattering cross-sections

    Energy Technology Data Exchange (ETDEWEB)

    Rusz, Ján, E-mail: jan.rusz@fysik.uu.se

    2017-06-15

    Highlights: • New algorithm for calculating double differential scattering cross-section. • Shown good convergence properties. • Outperforms older MATS algorithm, particularly in zone axis calculations. - Abstract: We present a new algorithm for calculating inelastic scattering cross-section for fast electrons. Compared to the previous Modified Automatic Term Selection (MATS) algorithm (Rusz et al. [18]), it has far better convergence properties in zone axis calculations and it allows to identify contributions of individual atoms. One can think of it as a blend of MATS algorithm and a method described by Weickenmeier and Kohl [10].

  11. Monte Carlo source convergence and the Whitesides problem

    International Nuclear Information System (INIS)

    Blomquist, R. N.

    2000-01-01

    The issue of fission source convergence in Monte Carlo eigenvalue calculations is of interest because of the potential consequences of erroneous criticality safety calculations. In this work, the authors compare two different techniques to improve the source convergence behavior of standard Monte Carlo calculations applied to challenging source convergence problems. The first method, super-history powering, attempts to avoid discarding important fission sites between generations by delaying stochastic sampling of the fission site bank until after several generations of multiplication. The second method, stratified sampling of the fission site bank, explicitly keeps the important sites even if conventional sampling would have eliminated them. The test problems are variants of Whitesides' Criticality of the World problem in which the fission site phase space was intentionally undersampled in order to induce marginally intolerable variability in local fission site populations. Three variants of the problem were studied, each with a different degree of coupling between fissionable pieces. Both the superhistory powering method and the stratified sampling method were shown to improve convergence behavior, although stratified sampling is more robust for the extreme case of no coupling. Neither algorithm completely eliminates the loss of the most important fissionable piece, and if coupling is absent, the lost piece cannot be recovered unless its sites from earlier generations have been retained. Finally, criteria for measuring source convergence reliability are proposed and applied to the test problems

  12. Error bounds for augmented truncations of discrete-time block-monotone Markov chains under subgeometric drift conditions

    OpenAIRE

    Masuyama, Hiroyuki

    2015-01-01

    This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeometric drift conditions. The main result of this paper is to present an upper bound for the total variation distance between the stationary probability vectors of a block-monotone Markov chain and its LC-block-augmented truncation. The main result is extended to Markov chains that themselves may not be block monoton...

  13. Parameter identification based on modified simulated annealing differential evolution algorithm for giant magnetostrictive actuator

    Science.gov (United States)

    Gao, Xiaohui; Liu, Yongguang

    2018-01-01

    There is a serious nonlinear relationship between input and output in the giant magnetostrictive actuator (GMA) and how to establish mathematical model and identify its parameters is very important to study characteristics and improve control accuracy. The current-displacement model is firstly built based on Jiles-Atherton (J-A) model theory, Ampere loop theorem and stress-magnetism coupling model. And then laws between unknown parameters and hysteresis loops are studied to determine the data-taking scope. The modified simulated annealing differential evolution algorithm (MSADEA) is proposed by taking full advantage of differential evolution algorithm's fast convergence and simulated annealing algorithm's jumping property to enhance the convergence speed and performance. Simulation and experiment results shows that this algorithm is not only simple and efficient, but also has fast convergence speed and high identification accuracy.

  14. Pathwise duals of monotone and additive Markov processes

    Czech Academy of Sciences Publication Activity Database

    Sturm, A.; Swart, Jan M.

    -, - (2018) ISSN 0894-9840 R&D Projects: GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : pathwise duality * monotone Markov process * additive Markov process * interacting particle system Subject RIV: BA - General Mathematics Impact factor: 0.854, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf

  15. The relation between majorization theory and quantum information from entanglement monotones perspective

    Energy Technology Data Exchange (ETDEWEB)

    Erol, V. [Department of Computer Engineering, Institute of Science, Okan University, Istanbul (Turkey); Netas Telecommunication Inc., Istanbul (Turkey)

    2016-04-21

    Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.

  16. Phase retrieval via incremental truncated amplitude flow algorithm

    Science.gov (United States)

    Zhang, Quanbing; Wang, Zhifa; Wang, Linjie; Cheng, Shichao

    2017-10-01

    This paper considers the phase retrieval problem of recovering the unknown signal from the given quadratic measurements. A phase retrieval algorithm based on Incremental Truncated Amplitude Flow (ITAF) which combines the ITWF algorithm and the TAF algorithm is proposed. The proposed ITAF algorithm enhances the initialization by performing both of the truncation methods used in ITWF and TAF respectively, and improves the performance in the gradient stage by applying the incremental method proposed in ITWF to the loop stage of TAF. Moreover, the original sampling vector and measurements are preprocessed before initialization according to the variance of the sensing matrix. Simulation experiments verified the feasibility and validity of the proposed ITAF algorithm. The experimental results show that it can obtain higher success rate and faster convergence speed compared with other algorithms. Especially, for the noiseless random Gaussian signals, ITAF can recover any real-valued signal accurately from the magnitude measurements whose number is about 2.5 times of the signal length, which is close to the theoretic limit (about 2 times of the signal length). And it usually converges to the optimal solution within 20 iterations which is much less than the state-of-the-art algorithms.

  17. Generalized monotonicity from global minimization in fourth-order ODEs

    NARCIS (Netherlands)

    M.A. Peletier (Mark)

    2000-01-01

    textabstractWe consider solutions of the stationary Extended Fisher-Kolmogorov equation with general potential that are global minimizers of an associated variational problem. We present results that relate the global minimization property to a generalized concept of monotonicity of the solutions.

  18. Acceleration of the direct reconstruction of linear parametric images using nested algorithms

    International Nuclear Information System (INIS)

    Wang Guobao; Qi Jinyi

    2010-01-01

    Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

  19. Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

    Science.gov (United States)

    Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

    2018-06-01

    In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

  20. Golden Sine Algorithm: A Novel Math-Inspired Algorithm

    Directory of Open Access Journals (Sweden)

    TANYILDIZI, E.

    2017-05-01

    Full Text Available In this study, Golden Sine Algorithm (Gold-SA is presented as a new metaheuristic method for solving optimization problems. Gold-SA has been developed as a new search algorithm based on population. This math-based algorithm is inspired by sine that is a trigonometric function. In the algorithm, random individuals are created as many as the number of search agents with uniform distribution for each dimension. The Gold-SA operator searches to achieve a better solution in each iteration by trying to bring the current situation closer to the target value. The solution space is narrowed by the golden section so that the areas that are supposed to give only good results are scanned instead of the whole solution space scan. In the tests performed, it is seen that Gold-SA has better results than other population based methods. In addition, Gold-SA has fewer algorithm-dependent parameters and operators than other metaheuristic methods, increasing the importance of this method by providing faster convergence of this new method.

  1. Stability and convergence analysis of the quasi-dynamics method for the initial pebble packing

    International Nuclear Information System (INIS)

    Li, Y.; Ji, W.

    2012-01-01

    The simulation for the pebble flow recirculation within Pebble Bed Reactors (PBRs) requires an efficient algorithm to generate an initial overlap-free pebble configuration within the reactor core. In the previous work, a dynamics-based approach, the Quasi-Dynamics Method (QDM), has been proposed to generate densely distributed pebbles in PBRs with cylindrical and annular core geometries. However, the stability and the efficiency of the QDM were not fully addressed. In this work, the algorithm is reformulated with two control parameters and the impact of these parameters on the algorithm performance is investigated. Firstly, the theoretical analysis for a 1-D packing system is conducted and the range of the parameter in which the algorithm is convergent is estimated. Then, this estimation is verified numerically for a 3-D packing system. Finally, the algorithm is applied to modeling the PBR fuel loading configuration and the convergence performance at different packing fractions is presented. Results show that the QDM is efficient in packing pebbles within the realistic range of the packing fraction in PBRs, and it is capable in handling cylindrical geometry with packing fractions up to 63.5%. (authors)

  2. Statistical image reconstruction for transmission tomography using relaxed ordered subset algorithms

    International Nuclear Information System (INIS)

    Kole, J S

    2005-01-01

    Statistical reconstruction methods offer possibilities for improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications in x-ray computed tomography (CT). To reduce reconstruction times, we have applied (under) relaxation to ordered subset algorithms. This enables us to use subsets consisting of only single projection angle, effectively increasing the number of image updates within an entire iteration. A second advantage of applying relaxation is that it can help improve convergence by removing the limit cycle behaviour of ordered subset algorithms, which normally do not converge to an optimal solution but rather a suboptimal limit cycle consisting of as many points as there are subsets. Relaxation suppresses the limit cycle behaviour by decreasing the stepsize for approaching the solution. A simulation study for a 2D mathematical phantom and three different ordered subset algorithms shows that all three algorithms benefit from relaxation: equal noise-to-resolution trade-off can be achieved using fewer iterations than the conventional algorithms, while a lower minimal normalized mean square error (NMSE) clearly indicates a better convergence. Two different schemes for setting the relaxation parameter are studied, and both schemes yield approximately the same minimal NMSE

  3. Smooth Approximation l 0-Norm Constrained Affine Projection Algorithm and Its Applications in Sparse Channel Estimation

    Science.gov (United States)

    2014-01-01

    We propose a smooth approximation l 0-norm constrained affine projection algorithm (SL0-APA) to improve the convergence speed and the steady-state error of affine projection algorithm (APA) for sparse channel estimation. The proposed algorithm ensures improved performance in terms of the convergence speed and the steady-state error via the combination of a smooth approximation l 0-norm (SL0) penalty on the coefficients into the standard APA cost function, which gives rise to a zero attractor that promotes the sparsity of the channel taps in the channel estimation and hence accelerates the convergence speed and reduces the steady-state error when the channel is sparse. The simulation results demonstrate that our proposed SL0-APA is superior to the standard APA and its sparsity-aware algorithms in terms of both the convergence speed and the steady-state behavior in a designated sparse channel. Furthermore, SL0-APA is shown to have smaller steady-state error than the previously proposed sparsity-aware algorithms when the number of nonzero taps in the sparse channel increases. PMID:24790588

  4. Convergence accommodation to convergence CA/C ratio: convergence versus divergence.

    Science.gov (United States)

    Simmons, Joshua M; Firth, Alison Y

    2014-09-01

    To determine whether the convergence accommodation to convergence (CA/C) ratio during divergence with base-in (BI) prisms is of a similar or different magnitude to that measured during convergence with base-out (BO) prisms. Eighteen participants with normal binocular single vision were recruited. The participants viewed a pseudo-Gaussian target, which consisted of a light emitting diode (LED) behind a diffusing screen at 40 cm. After 5 minutes of dark adaptation, the refractive status of the eye was measured without any prism using a Shin-Nippon SRW-5000 autorefractor. The participant held the selected prism (5Δ or 10Δ BO or BI, counterbalanced) in front of their right eye and obtained a single, fused image of the target while refractive measures were taken with each. A 30-second rest period was given between measurements. The mean age of the participants was 20.6±3.22 years. The mean CA/C ratios for the 5Δ BO, 10Δ BO, 5Δ BI, and 10Δ BI were 0.108 (±0.074) D/Δ, 0.110 (±0.056) D/Δ, 0.100 (±0.090) D/Δ, and 0.089 (±0.055) D/Δ, respectively. A 2-factor repeated measures ANOVA found that the CA/C ratio did not significantly change with differing levels of prism-induced convergence and divergence (p=0.649). Change in accommodation induced by manipulating vergence is similar whether convergence or divergence are induced. The CA/C ratio did not show any change with differing levels of prism-induced convergence and divergence.

  5. Absolute Monotonicity of Functions Related To Estimates of First Eigenvalue of Laplace Operator on Riemannian Manifolds

    Directory of Open Access Journals (Sweden)

    Feng Qi

    2014-10-01

    Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.

  6. Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients

    KAUST Repository

    Matevosyan, Norayr

    2010-10-21

    In this paper we extend the results of Caffarelli, Jerison, and Kenig [Ann. of Math. (2)155 (2002)] and Caffarelli and Kenig [Amer. J. Math.120 (1998)] by establishing an almost monotonicity estimate for pairs of continuous functions satisfying u± ≥ 0 Lu± ≥ -1, u+ · u_ = 0 ;in an infinite strip (global version) or a finite parabolic cylinder (localized version), where L is a uniformly parabolic operator Lu = LA,b,cu := div(A(x, s)∇u) + b(x,s) · ∇u + c(x,s)u - δsu with double Dini continuous A and uniformly bounded b and c. We also prove the elliptic counterpart of this estimate.This closes the gap between the known conditions in the literature (both in the elliptic and parabolic case) imposed on u± in order to obtain an almost monotonicity estimate.At the end of the paper, we demonstrate how to use this new almost monotonicity formula to prove the optimal C1,1-regularity in a fairly general class of quasi-linear obstacle-type free boundary problems. © 2010 Wiley Periodicals, Inc.

  7. A new BP Fourier algorithm and its application in English teaching evaluation

    Science.gov (United States)

    Pei, Xuehui; Pei, Guixin

    2017-08-01

    BP neural network algorithm has wide adaptability and accuracy when used in complicated system evaluation, but its calculation defects such as slow convergence have limited its practical application. The paper tries to speed up the calculation convergence of BP neural network algorithm with Fourier basis functions and presents a new BP Fourier algorithm for complicated system evaluation. First, shortages and working principle of BP algorithm are analyzed for subsequent targeted improvement; Second, the presented BP Fourier algorithm adopts Fourier basis functions to simplify calculation structure, designs new calculation transfer function between input and output layers, and conducts theoretical analysis to prove the efficiency of the presented algorithm; Finally, the presented algorithm is used in evaluating university English teaching and the application results shows that the presented BP Fourier algorithm has better performance in calculation efficiency and evaluation accuracy and can be used in evaluating complicated system practically.

  8. Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

    International Nuclear Information System (INIS)

    Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

    2012-01-01

    We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. (paper)

  9. An enhanced search algorithm for the charged fuel enrichment in equilibrium cycle analysis of REBUS-3

    International Nuclear Information System (INIS)

    Park, Tongkyu; Yang, Won Sik; Kim, Sang-Ji

    2017-01-01

    Highlights: • An enhanced search algorithm for charged fuel enrichment was developed for equilibrium cycle analysis with REBUS-3. • The new search algorithm is not sensitive to the user-specified initial guesses. • The new algorithm reduces the computational time by a factor of 2–3. - Abstract: This paper presents an enhanced search algorithm for the charged fuel enrichment in equilibrium cycle analysis of REBUS-3. The current enrichment search algorithm of REBUS-3 takes a large number of iterations to yield a converged solution or even terminates without a converged solution when the user-specified initial guesses are far from the solution. To resolve the convergence problem and to reduce the computational time, an enhanced search algorithm was developed. The enhanced algorithm is based on the idea of minimizing the number of enrichment estimates by allowing drastic enrichment changes and by optimizing the current search algorithm of REBUS-3. Three equilibrium cycle problems with recycling, without recycling and of high discharge burnup were defined and a series of sensitivity analyses were performed with a wide range of user-specified initial guesses. Test results showed that the enhanced search algorithm is able to produce a converged solution regardless of the initial guesses. In addition, it was able to reduce the number of flux calculations by a factor of 2.9, 1.8, and 1.7 for equilibrium cycle problems with recycling, without recycling, and of high discharge burnup, respectively, compared to the current search algorithm.

  10. Proportionate Minimum Error Entropy Algorithm for Sparse System Identification

    Directory of Open Access Journals (Sweden)

    Zongze Wu

    2015-08-01

    Full Text Available Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.

  11. Fast treatment plan modification with an over-relaxed Cimmino algorithm

    International Nuclear Information System (INIS)

    Wu Chuan; Jeraj, Robert; Lu Weiguo; Mackie, Thomas R.

    2004-01-01

    A method to quickly modify a treatment plan in adaptive radiotherapy was proposed and studied. The method is based on a Cimmino-type algorithm in linear programming. The fast convergence speed is achieved by over-relaxing the algorithm relaxation parameter from its sufficient convergence range of (0, 2) to (0, ∞). The algorithm parameters are selected so that the over-relaxed Cimmino (ORC) algorithm can effectively approximate an unconstrained re-optimization process in adaptive radiotherapy. To demonstrate the effectiveness and flexibility of the proposed method in adaptive radiotherapy, two scenarios with different organ motion/deformation of one nasopharyngeal case were presented with comparisons made between this method and the re-optimization method. In both scenarios, the ORC algorithm modified treatment plans have dose distributions that are similar to those given by the re-optimized treatment plans. It takes us using the ORC algorithm to finish a treatment plan modification at least three times faster than the re-optimization procedure compared

  12. Convergence properties of iterative algorithms for solving the nodal diffusion equations

    International Nuclear Information System (INIS)

    Azmy, Y.Y.; Kirk, B.L.

    1990-01-01

    We drive the five point form of the nodal diffusion equations in two-dimensional Cartesian geometry and develop three iterative schemes to solve the discrete-variable equations: the unaccelerated, partial Successive Over Relaxation (SOR), and the full SOR methods. By decomposing the iteration error into its Fourier modes, we determine the spectral radius of each method for infinite medium, uniform model problems, and for the unaccelerated and partial SOR methods for finite medium, uniform model problems. Also for the two variants of the SOR method we determine the optimal relaxation factor that results in the smallest number of iterations required for convergence. Our results indicate that the number of iterations for the unaccelerated and partial SOR methods is second order in the number of nodes per dimension, while, for the full SOR this behavior is first order, resulting in much faster convergence for very large problems. We successfully verify the results of the spectral analysis against those of numerical experiments, and we show that for the full SOR method the linear dependence of the number of iterations on the number of nodes per dimension is relatively insensitive to the value of the relaxation parameter, and that it remains linear even for heterogenous problems. 14 refs., 1 fig

  13. Neutronic rebalance algorithms for SIMMER

    International Nuclear Information System (INIS)

    Soran, P.D.

    1976-05-01

    Four algorithms to solve the two-dimensional neutronic rebalance equations in SIMMER are investigated. Results of the study are presented and indicate that a matrix decomposition technique with a variable convergence criterion is the best solution algorithm in terms of accuracy and calculational speed. Rebalance numerical stability problems are examined. The results of the study can be applied to other neutron transport codes which use discrete ordinates techniques

  14. Coarse Alignment Technology on Moving base for SINS Based on the Improved Quaternion Filter Algorithm.

    Science.gov (United States)

    Zhang, Tao; Zhu, Yongyun; Zhou, Feng; Yan, Yaxiong; Tong, Jinwu

    2017-06-17

    Initial alignment of the strapdown inertial navigation system (SINS) is intended to determine the initial attitude matrix in a short time with certain accuracy. The alignment accuracy of the quaternion filter algorithm is remarkable, but the convergence rate is slow. To solve this problem, this paper proposes an improved quaternion filter algorithm for faster initial alignment based on the error model of the quaternion filter algorithm. The improved quaternion filter algorithm constructs the K matrix based on the principle of optimal quaternion algorithm, and rebuilds the measurement model by containing acceleration and velocity errors to make the convergence rate faster. A doppler velocity log (DVL) provides the reference velocity for the improved quaternion filter alignment algorithm. In order to demonstrate the performance of the improved quaternion filter algorithm in the field, a turntable experiment and a vehicle test are carried out. The results of the experiments show that the convergence rate of the proposed improved quaternion filter is faster than that of the tradition quaternion filter algorithm. In addition, the improved quaternion filter algorithm also demonstrates advantages in terms of correctness, effectiveness, and practicability.

  15. Novel Adaptive Bacteria Foraging Algorithms for Global Optimization

    Directory of Open Access Journals (Sweden)

    Ahmad N. K. Nasir

    2014-01-01

    Full Text Available This paper presents improved versions of bacterial foraging algorithm (BFA. The chemotaxis feature of bacteria through random motion is an effective strategy for exploring the optimum point in a search area. The selection of small step size value in the bacteria motion leads to high accuracy in the solution but it offers slow convergence. On the contrary, defining a large step size in the motion provides faster convergence but the bacteria will be unable to locate the optimum point hence reducing the fitness accuracy. In order to overcome such problems, novel linear and nonlinear mathematical relationships based on the index of iteration, index of bacteria, and fitness cost are adopted which can dynamically vary the step size of bacteria movement. The proposed algorithms are tested with several unimodal and multimodal benchmark functions in comparison with the original BFA. Moreover, the application of the proposed algorithms in modelling of a twin rotor system is presented. The results show that the proposed algorithms outperform the predecessor algorithm in all test functions and acquire better model for the twin rotor system.

  16. Efficient solution to the stagnation problem of the particle swarm optimization algorithm for phase diversity.

    Science.gov (United States)

    Qi, Xin; Ju, Guohao; Xu, Shuyan

    2018-04-10

    The phase diversity (PD) technique needs optimization algorithms to minimize the error metric and find the global minimum. Particle swarm optimization (PSO) is very suitable for PD due to its simple structure, fast convergence, and global searching ability. However, the traditional PSO algorithm for PD still suffers from the stagnation problem (premature convergence), which can result in a wrong solution. In this paper, the stagnation problem of the traditional PSO algorithm for PD is illustrated first. Then, an explicit strategy is proposed to solve this problem, based on an in-depth understanding of the inherent optimization mechanism of the PSO algorithm. Specifically, a criterion is proposed to detect premature convergence; then a redistributing mechanism is proposed to prevent premature convergence. To improve the efficiency of this redistributing mechanism, randomized Halton sequences are further introduced to ensure the uniform distribution and randomness of the redistributed particles in the search space. Simulation results show that this strategy can effectively solve the stagnation problem of the PSO algorithm for PD, especially for large-scale and high-dimension wavefront sensing and noisy conditions. This work is further verified by an experiment. This work can improve the robustness and performance of PD wavefront sensing.

  17. Optimizer convergence and local minima errors and their clinical importance

    International Nuclear Information System (INIS)

    Jeraj, Robert; Wu, Chuan; Mackie, Thomas R

    2003-01-01

    Two of the errors common in the inverse treatment planning optimization have been investigated. The first error is the optimizer convergence error, which appears because of non-perfect convergence to the global or local solution, usually caused by a non-zero stopping criterion. The second error is the local minima error, which occurs when the objective function is not convex and/or the feasible solution space is not convex. The magnitude of the errors, their relative importance in comparison to other errors as well as their clinical significance in terms of tumour control probability (TCP) and normal tissue complication probability (NTCP) were investigated. Two inherently different optimizers, a stochastic simulated annealing and deterministic gradient method were compared on a clinical example. It was found that for typical optimization the optimizer convergence errors are rather small, especially compared to other convergence errors, e.g., convergence errors due to inaccuracy of the current dose calculation algorithms. This indicates that stopping criteria could often be relaxed leading into optimization speed-ups. The local minima errors were also found to be relatively small and typically in the range of the dose calculation convergence errors. Even for the cases where significantly higher objective function scores were obtained the local minima errors were not significantly higher. Clinical evaluation of the optimizer convergence error showed good correlation between the convergence of the clinical TCP or NTCP measures and convergence of the physical dose distribution. On the other hand, the local minima errors resulted in significantly different TCP or NTCP values (up to a factor of 2) indicating clinical importance of the local minima produced by physical optimization

  18. Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables

    KAUST Repository

    Chikalov, Igor

    2013-01-01

    In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct experiments. We show that, for each monotone Boolean function with at most five variables, there exists a totally optimal decision tree which is optimal with respect to both depth and number of nodes.

  19. Classification algorithms using adaptive partitioning

    KAUST Repository

    Binev, Peter; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald

    2014-01-01

    © 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.

  20. Classification algorithms using adaptive partitioning

    KAUST Repository

    Binev, Peter

    2014-12-01

    © 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.

  1. An improved genetic algorithm with dynamic topology

    International Nuclear Information System (INIS)

    Cai Kai-Quan; Tang Yan-Wu; Zhang Xue-Jun; Guan Xiang-Min

    2016-01-01

    The genetic algorithm (GA) is a nature-inspired evolutionary algorithm to find optima in search space via the interaction of individuals. Recently, researchers demonstrated that the interaction topology plays an important role in information exchange among individuals of evolutionary algorithm. In this paper, we investigate the effect of different network topologies adopted to represent the interaction structures. It is found that GA with a high-density topology ends up more likely with an unsatisfactory solution, contrarily, a low-density topology can impede convergence. Consequently, we propose an improved GA with dynamic topology, named DT-GA, in which the topology structure varies dynamically along with the fitness evolution. Several experiments executed with 15 well-known test functions have illustrated that DT-GA outperforms other test GAs for making a balance of convergence speed and optimum quality. Our work may have implications in the combination of complex networks and computational intelligence. (paper)

  2. Quantum Behaved Particle Swarm Optimization Algorithm Based on Artificial Fish Swarm

    OpenAIRE

    Yumin, Dong; Li, Zhao

    2014-01-01

    Quantum behaved particle swarm algorithm is a new intelligent optimization algorithm; the algorithm has less parameters and is easily implemented. In view of the existing quantum behaved particle swarm optimization algorithm for the premature convergence problem, put forward a quantum particle swarm optimization algorithm based on artificial fish swarm. The new algorithm based on quantum behaved particle swarm algorithm, introducing the swarm and following activities, meanwhile using the a...

  3. An Orthogonal Multi-Swarm Cooperative PSO Algorithm with a Particle Trajectory Knowledge Base

    Directory of Open Access Journals (Sweden)

    Jun Yang

    2017-01-01

    Full Text Available A novel orthogonal multi-swarm cooperative particle swarm optimization (PSO algorithm with a particle trajectory knowledge base is presented in this paper. Different from the traditional PSO algorithms and other variants of PSO, the proposed orthogonal multi-swarm cooperative PSO algorithm not only introduces an orthogonal initialization mechanism and a particle trajectory knowledge base for multi-dimensional optimization problems, but also conceives a new adaptive cooperation mechanism to accomplish the information interaction among swarms and particles. Experiments are conducted on a set of benchmark functions, and the results show its better performance compared with traditional PSO algorithm in aspects of convergence, computational efficiency and avoiding premature convergence.

  4. A homotopy algorithm for digital optimal projection control GASD-HADOC

    Science.gov (United States)

    Collins, Emmanuel G., Jr.; Richter, Stephen; Davis, Lawrence D.

    1993-01-01

    The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

  5. Fully 3D PET image reconstruction using a fourier preconditioned conjugate-gradient algorithm

    International Nuclear Information System (INIS)

    Fessler, J.A.; Ficaro, E.P.

    1996-01-01

    Since the data sizes in fully 3D PET imaging are very large, iterative image reconstruction algorithms must converge in very few iterations to be useful. One can improve the convergence rate of the conjugate-gradient (CG) algorithm by incorporating preconditioning operators that approximate the inverse of the Hessian of the objective function. If the 3D cylindrical PET geometry were not truncated at the ends, then the Hessian of the penalized least-squares objective function would be approximately shift-invariant, i.e. G'G would be nearly block-circulant, where G is the system matrix. We propose a Fourier preconditioner based on this shift-invariant approximation to the Hessian. Results show that this preconditioner significantly accelerates the convergence of the CG algorithm with only a small increase in computation

  6. Multiplier convergent series and uniform convergence of mapping ...

    Indian Academy of Sciences (India)

    MS received 14 April 2011; revised 17 November 2012. Abstract. In this paper, we introduce the frame property of complex sequence sets and study the uniform convergence of nonlinear mapping series in β-dual of spaces consisting of multiplier convergent series. Keywords. Multiplier convergent series; mapping series. 1.

  7. The serial message-passing schedule for LDPC decoding algorithms

    Science.gov (United States)

    Liu, Mingshan; Liu, Shanshan; Zhou, Yuan; Jiang, Xue

    2015-12-01

    The conventional message-passing schedule for LDPC decoding algorithms is the so-called flooding schedule. It has the disadvantage that the updated messages cannot be used until next iteration, thus reducing the convergence speed . In this case, the Layered Decoding algorithm (LBP) based on serial message-passing schedule is proposed. In this paper the decoding principle of LBP algorithm is briefly introduced, and then proposed its two improved algorithms, the grouped serial decoding algorithm (Grouped LBP) and the semi-serial decoding algorithm .They can improve LBP algorithm's decoding speed while maintaining a good decoding performance.

  8. Convergence Analysis of the Graph Allen-Cahn Scheme

    Science.gov (United States)

    2016-02-01

    steps Fdt(x) follows the same idea as above and involves only elementary calculations, we omit some of the details later. Next, we prove our main... linear as predicted by the 0.5 bound. Fig. 6.3: Two Moons Segmentation Problem. Left: Maximum stepsize for convergence, fixing = 1 varying N...semi- algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods. Mathematical Programming, 137

  9. Theoretical and experimental study of non-monotonous effects

    International Nuclear Information System (INIS)

    Delforge, J.

    1977-01-01

    In recent years, the study of the effects of low dose rates has expanded considerably, especially in connection with current problems concerning the environment and health physics. After having made a precise definition of the different types of non-monotonous effect which may be encountered, for each the main experimental results known are indicated, as well as the principal consequences which may be expected. One example is the case of radiotherapy, where there is a chance of finding irradiation conditions such that the ratio of destructive action on malignant cells to healthy cells is significantly improved. In the second part of the report, the appearance of these phenomena, especially at low dose rates are explained. For this purpose, the theory of transformation systems of P. Delattre is used as a theoretical framework. With the help of a specific example, it is shown that non-monotonous effects are frequently encountered, especially when the overall effect observed is actually the sum of several different elementary effects (e.g. in survival curves, where death may be due to several different causes), or when the objects studied possess inherent kinetics not limited to restoration phenomena alone (e.g. cellular cycle) [fr

  10. Proportionate-type normalized last mean square algorithms

    CERN Document Server

    Wagner, Kevin

    2013-01-01

    The topic of this book is proportionate-type normalized least mean squares (PtNLMS) adaptive filtering algorithms, which attempt to estimate an unknown impulse response by adaptively giving gains proportionate to an estimate of the impulse response and the current measured error. These algorithms offer low computational complexity and fast convergence times for sparse impulse responses in network and acoustic echo cancellation applications. New PtNLMS algorithms are developed by choosing gains that optimize user-defined criteria, such as mean square error, at all times. PtNLMS algorithms ar

  11. Dynamic training algorithm for dynamic neural networks

    International Nuclear Information System (INIS)

    Tan, Y.; Van Cauwenberghe, A.; Liu, Z.

    1996-01-01

    The widely used backpropagation algorithm for training neural networks based on the gradient descent has a significant drawback of slow convergence. A Gauss-Newton method based recursive least squares (RLS) type algorithm with dynamic error backpropagation is presented to speed-up the learning procedure of neural networks with local recurrent terms. Finally, simulation examples concerning the applications of the RLS type algorithm to identification of nonlinear processes using a local recurrent neural network are also included in this paper

  12. How do people learn from negative evidence? Non-monotonic generalizations and sampling assumptions in inductive reasoning.

    Science.gov (United States)

    Voorspoels, Wouter; Navarro, Daniel J; Perfors, Amy; Ransom, Keith; Storms, Gert

    2015-09-01

    A robust finding in category-based induction tasks is for positive observations to raise the willingness to generalize to other categories while negative observations lower the willingness to generalize. This pattern is referred to as monotonic generalization. Across three experiments we find systematic non-monotonicity effects, in which negative observations raise the willingness to generalize. Experiments 1 and 2 show that this effect emerges in hierarchically structured domains when a negative observation from a different category is added to a positive observation. They also demonstrate that this is related to a specific kind of shift in the reasoner's hypothesis space. Experiment 3 shows that the effect depends on the assumptions that the reasoner makes about how inductive arguments are constructed. Non-monotonic reasoning occurs when people believe the facts were put together by a helpful communicator, but monotonicity is restored when they believe the observations were sampled randomly from the environment. Copyright © 2015 Elsevier Inc. All rights reserved.

  13. New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

    Science.gov (United States)

    Bouchard, M

    2001-01-01

    In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

  14. Modified Projection Algorithms for Solving the Split Equality Problems

    Directory of Open Access Journals (Sweden)

    Qiao-Li Dong

    2014-01-01

    proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.

  15. A study of block algorithms for fermion matrix inversion

    International Nuclear Information System (INIS)

    Henty, D.

    1990-01-01

    We compare the convergence properties of Lanczos and Conjugate Gradient algorithms applied to the calculation of columns of the inverse fermion matrix for Kogut-Susskind and Wilson fermions in lattice QCD. When several columns of the inverse are required simultaneously, a block version of the Lanczos algorithm is most efficient at small mass, being over 5 times faster than the single algorithms. The block algorithm is also less susceptible to critical slowing down. (orig.)

  16. A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric

    DEFF Research Database (Denmark)

    Zimmermann, Ralf

    2017-01-01

    We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm...... converges locally and exhibits a linear rate of convergence....

  17. A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric

    OpenAIRE

    Zimmermann, Ralf

    2016-01-01

    We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear rate of convergence.

  18. Evolving Stochastic Learning Algorithm based on Tsallis entropic index

    Science.gov (United States)

    Anastasiadis, A. D.; Magoulas, G. D.

    2006-03-01

    In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight, and applies a form of noise that is characterized by the nonextensive entropic index q, regulated by a weight decay term. The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values. This is achieved by introducing a formula that defines a time-dependent relationship between these two important learning parameters. Our experimental study verifies that there are indeed improvements in the convergence speed of this new evolving stochastic learning algorithm, which makes learning faster than using the original Hybrid Learning Scheme (HLS). In addition, experiments are conducted to explore the influence of the entropic index q and temperature T on the convergence speed and stability of the proposed method.

  19. Three-phase Interstellar Medium in Galaxies Resolving Evolution with Star Formation and Supernova Feedback (TIGRESS): Algorithms, Fiducial Model, and Convergence

    Science.gov (United States)

    Kim, Chang-Goo; Ostriker, Eve C.

    2017-09-01

    We introduce TIGRESS, a novel framework for multi-physics numerical simulations of the star-forming interstellar medium (ISM) implemented in the Athena MHD code. The algorithms of TIGRESS are designed to spatially and temporally resolve key physical features, including: (1) the gravitational collapse and ongoing accretion of gas that leads to star formation in clusters; (2) the explosions of supernovae (SNe), both near their progenitor birth sites and from runaway OB stars, with time delays relative to star formation determined by population synthesis; (3) explicit evolution of SN remnants prior to the onset of cooling, which leads to the creation of the hot ISM; (4) photoelectric heating of the warm and cold phases of the ISM that tracks the time-dependent ambient FUV field from the young cluster population; (5) large-scale galactic differential rotation, which leads to epicyclic motion and shears out overdense structures, limiting large-scale gravitational collapse; (6) accurate evolution of magnetic fields, which can be important for vertical support of the ISM disk as well as angular momentum transport. We present tests of the newly implemented physics modules, and demonstrate application of TIGRESS in a fiducial model representing the solar neighborhood environment. We use a resolution study to demonstrate convergence and evaluate the minimum resolution {{Δ }}x required to correctly recover several ISM properties, including the star formation rate, wind mass-loss rate, disk scale height, turbulent and Alfvénic velocity dispersions, and volume fractions of warm and hot phases. For the solar neighborhood model, all these ISM properties are converged at {{Δ }}x≤slant 8 {pc}.

  20. The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

    Energy Technology Data Exchange (ETDEWEB)

    Ganapol, B.; Picca, P. [Dept. of Aerospace and Mechanical Engineering, Univ. of Arizona (United States); Previti, A.; Mostacci, D. [Laboratorio di Montecuccolino, Alma Mater Studiorum - Universita di Bologna (Italy)

    2012-07-01

    This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

  1. PS-FW: A Hybrid Algorithm Based on Particle Swarm and Fireworks for Global Optimization

    Science.gov (United States)

    Chen, Shuangqing; Wei, Lixin; Guan, Bing

    2018-01-01

    Particle swarm optimization (PSO) and fireworks algorithm (FWA) are two recently developed optimization methods which have been applied in various areas due to their simplicity and efficiency. However, when being applied to high-dimensional optimization problems, PSO algorithm may be trapped in the local optima owing to the lack of powerful global exploration capability, and fireworks algorithm is difficult to converge in some cases because of its relatively low local exploitation efficiency for noncore fireworks. In this paper, a hybrid algorithm called PS-FW is presented, in which the modified operators of FWA are embedded into the solving process of PSO. In the iteration process, the abandonment and supplement mechanism is adopted to balance the exploration and exploitation ability of PS-FW, and the modified explosion operator and the novel mutation operator are proposed to speed up the global convergence and to avoid prematurity. To verify the performance of the proposed PS-FW algorithm, 22 high-dimensional benchmark functions have been employed, and it is compared with PSO, FWA, stdPSO, CPSO, CLPSO, FIPS, Frankenstein, and ALWPSO algorithms. Results show that the PS-FW algorithm is an efficient, robust, and fast converging optimization method for solving global optimization problems. PMID:29675036

  2. Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application

    Science.gov (United States)

    Yang, Jian; Yang, Feng; Xi, Hong-Sheng; Guo, Wei; Sheng, Yanmin

    2007-12-01

    We propose a robust adaptive algorithm for generalized eigendecomposition problems that arise in modern signal processing applications. To that extent, the generalized eigendecomposition problem is reinterpreted as an unconstrained nonlinear optimization problem. Starting from the proposed cost function and making use of an approximation of the Hessian matrix, a robust modified Newton algorithm is derived. A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. The simulation results show that the proposed algorithm has fast convergence and excellent tracking capability, which are important in a practical time-varying communication environment.

  3. Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application

    Directory of Open Access Journals (Sweden)

    Yang Jian

    2007-01-01

    Full Text Available We propose a robust adaptive algorithm for generalized eigendecomposition problems that arise in modern signal processing applications. To that extent, the generalized eigendecomposition problem is reinterpreted as an unconstrained nonlinear optimization problem. Starting from the proposed cost function and making use of an approximation of the Hessian matrix, a robust modified Newton algorithm is derived. A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. The simulation results show that the proposed algorithm has fast convergence and excellent tracking capability, which are important in a practical time-varying communication environment.

  4. Modified Spectral Projected Subgradient Method: Convergence Analysis and Momentum Parameter Heuristics

    Directory of Open Access Journals (Sweden)

    Milagros Loreto

    2016-09-01

    Full Text Available The Modified Spectral Projected Subgradient (MSPS was proposed to solve Langrangen Dual Problems, and its convergence was shown when the momentum term was zero. The MSPS uses a momentum term in order to speed up its convergence. The momentum term is built on the multiplication of a momentum parameter and the direction of the previous iterate. In this work, we show convergence when the momentum parameter is a non-zero constant. We also propose heuristics to choose the momentum parameter intended to avoid the Zigzagging Phenomenon of Kind I. This phenomenon is present in the MSPS when at an iterate the subgradient forms an obtuse angle with the previous direction. We identify and diminish the Zigzagging Phenomenon of Kind I on Setcovering problems, and compare our numerical results to those of the original MSPS algorithm.

  5. On convergence rates for iteratively regularized procedures with linear penalty terms

    International Nuclear Information System (INIS)

    Smirnova, Alexandra

    2012-01-01

    The impact of this paper is twofold. First, we study convergence rates of the iteratively regularized Gauss–Newton (IRGN) algorithm with a linear penalty term under a generalized source assumption and show how the regularizing properties of new iterations depend on the solution smoothness. Secondly, we introduce an adaptive IRGN procedure, which is investigated under a relaxed smoothness condition. The introduction and analysis of a more general penalty term are of great importance since, apart from bringing stability to the numerical scheme designed for solving a large class of applied inverse problems, it allows us to incorporate various types of a priori information available on the model. Both a priori and a posteriori stopping rules are investigated. For the a priori stopping rule, optimal convergence rates are derived. A numerical example illustrating convergence rates is considered. (paper)

  6. Convergent Power Series of sech⁡(x and Solutions to Nonlinear Differential Equations

    Directory of Open Access Journals (Sweden)

    U. Al Khawaja

    2018-01-01

    Full Text Available It is known that power series expansion of certain functions such as sech⁡(x diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS to obtain a power series representation of sech⁡(x that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2. A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.

  7. Statistical analysis of sediment toxicity by additive monotone regression splines

    NARCIS (Netherlands)

    Boer, de W.J.; Besten, den P.J.; Braak, ter C.J.F.

    2002-01-01

    Modeling nonlinearity and thresholds in dose-effect relations is a major challenge, particularly in noisy data sets. Here we show the utility of nonlinear regression with additive monotone regression splines. These splines lead almost automatically to the estimation of thresholds. We applied this

  8. Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability

    International Nuclear Information System (INIS)

    Bogdanov, I I; Guterman, A E

    2007-01-01

    Bijective linear transformations of the matrix algebra over an arbitrary field that preserve simultaneous diagonalizability are characterized. This result is used for the characterization of bijective linear monotone transformations . Bibliography: 28 titles.

  9. Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals

    International Nuclear Information System (INIS)

    Kubin, L.P.; Sauzay, M.

    2011-01-01

    This work reviews and critically discusses the current understanding of two scaling laws, which are ubiquitous in the modeling of monotonic plastic deformation in face-centered cubic metals. A compilation of the available data allows extending the domain of application of these scaling laws to cyclic deformation. The strengthening relation tells that the flow stress is proportional to the square root of the average dislocation density, whereas the similitude relation assumes that the flow stress is inversely proportional to the characteristic wavelength of dislocation patterns. The strengthening relation arises from short-range reactions of non-coplanar segments and applies all through the first three stages of the monotonic stress vs. strain curves. The value of the proportionality coefficient is calculated and simulated in good agreement with the bulk of experimental measurements published since the beginning of the 1960's. The physical origin of what is called similitude is not understood and the related coefficient is not predictable. Its value is determined from a review of the experimental literature. The generalization of these scaling laws to cyclic deformation is carried out on the base of a large collection of experimental results on single and polycrystals of various materials and on different microstructures. Surprisingly, for persistent slip bands (PSBs), both the strengthening and similitude coefficients appear to be more than two times smaller than the corresponding monotonic values, whereas their ratio is the same as in monotonic deformation. The similitude relation is also checked in cell structures and in labyrinth structures. Under low cyclic stresses, the strengthening coefficient is found even lower than in PSBs. A tentative explanation is proposed for the differences observed between cyclic and monotonic deformation. Finally, the influence of cross-slip on the temperature dependence of the saturation stress of PSBs is discussed in some detail

  10. Monotonicity properties of keff with shape change and with nesting

    International Nuclear Information System (INIS)

    Arzhanov, V.

    2002-01-01

    It was found that, contrary to expectations based on physical intuition, k eff can both increase and decrease when changing the shape of an initially regular critical system, while preserving its volume. Physical intuition would only allow for a decrease of k eff when the surface/volume ratio increases. The unexpected behaviour of increasing k eff was found through numerical investigation. For a convincing demonstration of the possibility of the non-monotonic behaviour, a simple geometrical proof was constructed. This latter proof, in turn, is based on the assumption that k eff can only increase (or stay constant) in the case of nesting, i.e. when adding extra volume to a system. Since we found no formal proof of the nesting theorem for the general case, we close the paper by a simple formal proof of the monotonic behaviour of k eff by nesting

  11. Statistical behaviour of adaptive multilevel splitting algorithms in simple models

    International Nuclear Information System (INIS)

    Rolland, Joran; Simonnet, Eric

    2015-01-01

    Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection–mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenomenon and show logarithmic convergence of the trajectory durations

  12. Monotone difference schemes for weakly coupled elliptic and parabolic systems

    NARCIS (Netherlands)

    P. Matus (Piotr); F.J. Gaspar Lorenz (Franscisco); L. M. Hieu (Le Minh); V.T.K. Tuyen (Vo Thi Kim)

    2017-01-01

    textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is

  13. Cognitive radio resource allocation based on coupled chaotic genetic algorithm

    International Nuclear Information System (INIS)

    Zu Yun-Xiao; Zhou Jie; Zeng Chang-Chang

    2010-01-01

    A coupled chaotic genetic algorithm for cognitive radio resource allocation which is based on genetic algorithm and coupled Logistic map is proposed. A fitness function for cognitive radio resource allocation is provided. Simulations are conducted for cognitive radio resource allocation by using the coupled chaotic genetic algorithm, simple genetic algorithm and dynamic allocation algorithm respectively. The simulation results show that, compared with simple genetic and dynamic allocation algorithm, coupled chaotic genetic algorithm reduces the total transmission power and bit error rate in cognitive radio system, and has faster convergence speed

  14. Hybrid Differential Dynamic Programming with Stochastic Search

    Science.gov (United States)

    Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob

    2016-01-01

    Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

  15. Automatic Regionalization Algorithm for Distributed State Estimation in Power Systems: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Dexin; Yang, Liuqing; Florita, Anthony; Alam, S.M. Shafiul; Elgindy, Tarek; Hodge, Bri-Mathias

    2016-08-01

    The deregulation of the power system and the incorporation of generation from renewable energy sources recessitates faster state estimation in the smart grid. Distributed state estimation (DSE) has become a promising and scalable solution to this urgent demand. In this paper, we investigate the regionalization algorithms for the power system, a necessary step before distributed state estimation can be performed. To the best of the authors' knowledge, this is the first investigation on automatic regionalization (AR). We propose three spectral clustering based AR algorithms. Simulations show that our proposed algorithms outperform the two investigated manual regionalization cases. With the help of AR algorithms, we also show how the number of regions impacts the accuracy and convergence speed of the DSE and conclude that the number of regions needs to be chosen carefully to improve the convergence speed of DSEs.

  16. A new LMS algorithm for analysis of atrial fibrillation signals.

    Science.gov (United States)

    Ciaccio, Edward J; Biviano, Angelo B; Whang, William; Garan, Hasan

    2012-03-26

    A biomedical signal can be defined by its extrinsic features (x-axis and y-axis shift and scale) and intrinsic features (shape after normalization of extrinsic features). In this study, an LMS algorithm utilizing the method of differential steepest descent is developed, and is tested by normalization of extrinsic features in complex fractionated atrial electrograms (CFAE). Equations for normalization of x-axis and y-axis shift and scale are first derived. The algorithm is implemented for real-time analysis of CFAE acquired during atrial fibrillation (AF). Data was acquired at a 977 Hz sampling rate from 10 paroxysmal and 10 persistent AF patients undergoing clinical electrophysiologic study and catheter ablation therapy. Over 24 trials, normalization characteristics using the new algorithm with four weights were compared to the Widrow-Hoff LMS algorithm with four tapped delays. The time for convergence, and the mean squared error (MSE) after convergence, were compared. The new LMS algorithm was also applied to lead aVF of the electrocardiogram in one patient with longstanding persistent AF, to enhance the F wave and to monitor extrinsic changes in signal shape. The average waveform over a 25 s interval was used as a prototypical reference signal for matching with the aVF lead. Based on the derivation equations, the y-shift and y-scale adjustments of the new LMS algorithm were shown to be equivalent to the scalar form of the Widrow-Hoff LMS algorithm. For x-shift and x-scale adjustments, rather than implementing a long tapped delay as in Widrow-Hoff LMS, the new method uses only two weights. After convergence, the MSE for matching paroxysmal CFAE averaged 0.46 ± 0.49 μV(2)/sample for the new LMS algorithm versus 0.72 ± 0.35 μV(2)/sample for Widrow-Hoff LMS. The MSE for matching persistent CFAE averaged 0.55 ± 0.95 μV(2)/sample for the new LMS algorithm versus 0.62 ± 0.55 μV(2)/sample for Widrow-Hoff LMS. There were no significant differences in estimation

  17. A new LMS algorithm for analysis of atrial fibrillation signals

    Directory of Open Access Journals (Sweden)

    Ciaccio Edward J

    2012-03-01

    Full Text Available Abstract Background A biomedical signal can be defined by its extrinsic features (x-axis and y-axis shift and scale and intrinsic features (shape after normalization of extrinsic features. In this study, an LMS algorithm utilizing the method of differential steepest descent is developed, and is tested by normalization of extrinsic features in complex fractionated atrial electrograms (CFAE. Method Equations for normalization of x-axis and y-axis shift and scale are first derived. The algorithm is implemented for real-time analysis of CFAE acquired during atrial fibrillation (AF. Data was acquired at a 977 Hz sampling rate from 10 paroxysmal and 10 persistent AF patients undergoing clinical electrophysiologic study and catheter ablation therapy. Over 24 trials, normalization characteristics using the new algorithm with four weights were compared to the Widrow-Hoff LMS algorithm with four tapped delays. The time for convergence, and the mean squared error (MSE after convergence, were compared. The new LMS algorithm was also applied to lead aVF of the electrocardiogram in one patient with longstanding persistent AF, to enhance the F wave and to monitor extrinsic changes in signal shape. The average waveform over a 25 s interval was used as a prototypical reference signal for matching with the aVF lead. Results Based on the derivation equations, the y-shift and y-scale adjustments of the new LMS algorithm were shown to be equivalent to the scalar form of the Widrow-Hoff LMS algorithm. For x-shift and x-scale adjustments, rather than implementing a long tapped delay as in Widrow-Hoff LMS, the new method uses only two weights. After convergence, the MSE for matching paroxysmal CFAE averaged 0.46 ± 0.49μV2/sample for the new LMS algorithm versus 0.72 ± 0.35μV2/sample for Widrow-Hoff LMS. The MSE for matching persistent CFAE averaged 0.55 ± 0.95μV2/sample for the new LMS algorithm versus 0.62 ± 0.55μV2/sample for Widrow

  18. An Improved DINEOF Algorithm for Filling Missing Values in Spatio-Temporal Sea Surface Temperature Data.

    Science.gov (United States)

    Ping, Bo; Su, Fenzhen; Meng, Yunshan

    2016-01-01

    In this study, an improved Data INterpolating Empirical Orthogonal Functions (DINEOF) algorithm for determination of missing values in a spatio-temporal dataset is presented. Compared with the ordinary DINEOF algorithm, the iterative reconstruction procedure until convergence based on every fixed EOF to determine the optimal EOF mode is not necessary and the convergence criterion is only reached once in the improved DINEOF algorithm. Moreover, in the ordinary DINEOF algorithm, after optimal EOF mode determination, the initial matrix with missing data will be iteratively reconstructed based on the optimal EOF mode until the reconstruction is convergent. However, the optimal EOF mode may be not the best EOF for some reconstructed matrices generated in the intermediate steps. Hence, instead of using asingle EOF to fill in the missing data, in the improved algorithm, the optimal EOFs for reconstruction are variable (because the optimal EOFs are variable, the improved algorithm is called VE-DINEOF algorithm in this study). To validate the accuracy of the VE-DINEOF algorithm, a sea surface temperature (SST) data set is reconstructed by using the DINEOF, I-DINEOF (proposed in 2015) and VE-DINEOF algorithms. Four parameters (Pearson correlation coefficient, signal-to-noise ratio, root-mean-square error, and mean absolute difference) are used as a measure of reconstructed accuracy. Compared with the DINEOF and I-DINEOF algorithms, the VE-DINEOF algorithm can significantly enhance the accuracy of reconstruction and shorten the computational time.

  19. A Data Forward Stepwise Fitting Algorithm Based on Orthogonal Function System

    Directory of Open Access Journals (Sweden)

    Li Han-Ju

    2017-01-01

    Full Text Available Data fitting is the main method of functional data analysis, and it is widely used in the fields of economy, social science, engineering technology and so on. Least square method is the main method of data fitting, but the least square method is not convergent, no memory property, big fitting error and it is easy to over fitting. Based on the orthogonal trigonometric function system, this paper presents a data forward stepwise fitting algorithm. This algorithm takes forward stepwise fitting strategy, each time using the nearest base function to fit the residual error generated by the previous base function fitting, which makes the residual mean square error minimum. In this paper, we theoretically prove the convergence, the memory property and the fitting error diminishing character for the algorithm. Experimental results show that the proposed algorithm is effective, and the fitting performance is better than that of the least square method and the forward stepwise fitting algorithm based on the non-orthogonal function system.

  20. Algorithms for worst-case tolerance optimization

    DEFF Research Database (Denmark)

    Schjær-Jacobsen, Hans; Madsen, Kaj

    1979-01-01

    New algorithms are presented for the solution of optimum tolerance assignment problems. The problems considered are defined mathematically as a worst-case problem (WCP), a fixed tolerance problem (FTP), and a variable tolerance problem (VTP). The basic optimization problem without tolerances...... is denoted the zero tolerance problem (ZTP). For solution of the WCP we suggest application of interval arithmetic and also alternative methods. For solution of the FTP an algorithm is suggested which is conceptually similar to algorithms previously developed by the authors for the ZTP. Finally, the VTP...... is solved by a double-iterative algorithm in which the inner iteration is performed by the FTP- algorithm. The application of the algorithm is demonstrated by means of relatively simple numerical examples. Basic properties, such as convergence properties, are displayed based on the examples....

  1. An Improved Hierarchical Genetic Algorithm for Sheet Cutting Scheduling with Process Constraints

    Directory of Open Access Journals (Sweden)

    Yunqing Rao

    2013-01-01

    Full Text Available For the first time, an improved hierarchical genetic algorithm for sheet cutting problem which involves n cutting patterns for m non-identical parallel machines with process constraints has been proposed in the integrated cutting stock model. The objective of the cutting scheduling problem is minimizing the weighted completed time. A mathematical model for this problem is presented, an improved hierarchical genetic algorithm (ant colony—hierarchical genetic algorithm is developed for better solution, and a hierarchical coding method is used based on the characteristics of the problem. Furthermore, to speed up convergence rates and resolve local convergence issues, a kind of adaptive crossover probability and mutation probability is used in this algorithm. The computational result and comparison prove that the presented approach is quite effective for the considered problem.

  2. An improved hierarchical genetic algorithm for sheet cutting scheduling with process constraints.

    Science.gov (United States)

    Rao, Yunqing; Qi, Dezhong; Li, Jinling

    2013-01-01

    For the first time, an improved hierarchical genetic algorithm for sheet cutting problem which involves n cutting patterns for m non-identical parallel machines with process constraints has been proposed in the integrated cutting stock model. The objective of the cutting scheduling problem is minimizing the weighted completed time. A mathematical model for this problem is presented, an improved hierarchical genetic algorithm (ant colony--hierarchical genetic algorithm) is developed for better solution, and a hierarchical coding method is used based on the characteristics of the problem. Furthermore, to speed up convergence rates and resolve local convergence issues, a kind of adaptive crossover probability and mutation probability is used in this algorithm. The computational result and comparison prove that the presented approach is quite effective for the considered problem.

  3. Research and Applications of Shop Scheduling Based on Genetic Algorithms

    Directory of Open Access Journals (Sweden)

    Hang ZHAO

    Full Text Available ABSTRACT Shop Scheduling is an important factor affecting the efficiency of production, efficient scheduling method and a research and application for optimization technology play an important role for manufacturing enterprises to improve production efficiency, reduce production costs and many other aspects. Existing studies have shown that improved genetic algorithm has solved the limitations that existed in the genetic algorithm, the objective function is able to meet customers' needs for shop scheduling, and the future research should focus on the combination of genetic algorithm with other optimized algorithms. In this paper, in order to overcome the shortcomings of early convergence of genetic algorithm and resolve local minimization problem in search process,aiming at mixed flow shop scheduling problem, an improved cyclic search genetic algorithm is put forward, and chromosome coding method and corresponding operation are given.The operation has the nature of inheriting the optimal individual ofthe previous generation and is able to avoid the emergence of local minimum, and cyclic and crossover operation and mutation operation can enhance the diversity of the population and then quickly get the optimal individual, and the effectiveness of the algorithm is validated. Experimental results show that the improved algorithm can well avoid the emergency of local minimum and is rapid in convergence.

  4. Monotone Comparative Statics for the Industry Composition

    DEFF Research Database (Denmark)

    Laugesen, Anders Rosenstand; Bache, Peter Arendorf

    2015-01-01

    We let heterogeneous firms face decisions on a number of complementary activities in a monopolistically-competitive industry. The endogenous level of competition and selection regarding entry and exit of firms introduces a wedge between monotone comparative statics (MCS) at the firm level and MCS...... for the industry composition. The latter phenomenon is defined as first-order stochastic dominance shifts in the equilibrium distributions of all activities across active firms. We provide sufficient conditions for MCS at both levels of analysis and show that we may have either type of MCS without the other...

  5. An electronic implementation for Liao's chaotic delayed neuron model with non-monotonous activation function

    International Nuclear Information System (INIS)

    Duan Shukai; Liao Xiaofeng

    2007-01-01

    A new chaotic delayed neuron model with non-monotonously increasing transfer function, called as chaotic Liao's delayed neuron model, was recently reported and analyzed. An electronic implementation of this model is described in detail. At the same time, some methods in circuit design, especially for circuit with time delayed unit and non-monotonously increasing activation unit, are also considered carefully. We find that the dynamical behaviors of the designed circuits are closely similar to the results predicted by numerical experiments

  6. The Sum-Product Algorithm for Degree-2 Check Nodes and Trapping Sets

    OpenAIRE

    Brevik, John O.; O'Sullivan, Michael E.

    2014-01-01

    The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the convergence of the algorithm are derived and applied to trapping sets.

  7. Sampling from a Discrete Distribution While Preserving Monotonicity.

    Science.gov (United States)

    1982-02-01

    in a table beforehand, this procedure, known as the inverse transform method, requires n storage spaces and EX comparisons on average, which may prove...limitations that deserve attention: a. In general, the alias method does not preserve a monotone relationship between U and X as does the inverse transform method...uses the inverse transform approach but with more information computed beforehand, as in the alias method. The proposed method is not new having been

  8. Martensitic Transformation in Ultrafine-Grained Stainless Steel AISI 304L Under Monotonic and Cyclic Loading

    Directory of Open Access Journals (Sweden)

    Heinz Werner Höppel

    2012-02-01

    Full Text Available The monotonic and cyclic deformation behavior of ultrafine-grained metastable austenitic steel AISI 304L, produced by severe plastic deformation, was investigated. Under monotonic loading, the martensitic phase transformation in the ultrafine-grained state is strongly favored. Under cyclic loading, the martensitic transformation behavior is similar to the coarse-grained condition, but the cyclic stress response is three times larger for the ultrafine-grained condition.

  9. Positivity and monotonicity properties of C0-semigroups. Pt. 1

    International Nuclear Information System (INIS)

    Bratteli, O.; Kishimoto, A.; Robinson, D.W.

    1980-01-01

    If exp(-tH), exp(-tK), are self-adjoint, positivity preserving, contraction semigroups on a Hilbert space H = L 2 (X;dμ) we write esup(-tH) >= esup(-tK) >= 0 whenever exp(-tH) - exp(-tK) is positivity preserving for all t >= 0 and then we characterize the class of positive functions for which (*) always implies esup(-tf(H)) >= esup(-tf(K)) >= 0. This class consists of the f epsilon Csup(infinitely)(0, infinitely) with (-1)sup(n)fsup((n + 1))(x) >= 0, x epsilon(0, infinitely), n = 0, 1, 2, ... In particular it contains the class of monotone operator functions. Furthermore if exp(-tH) is Lsup(P)(X;dμ) contractive for all p epsilon[1, infinitely] and all t > 0 (or, equivalently, for p = infinitely and t > 0) then exp(-tf(H)) has the same property. Various applications to monotonicity properties of Green's functions are given. (orig.)

  10. Non-monotonic effect of growth temperature on carrier collection in SnS solar cells

    International Nuclear Information System (INIS)

    Chakraborty, R.; Steinmann, V.; Mangan, N. M.; Brandt, R. E.; Poindexter, J. R.; Jaramillo, R.; Mailoa, J. P.; Hartman, K.; Polizzotti, A.; Buonassisi, T.; Yang, C.; Gordon, R. G.

    2015-01-01

    We quantify the effects of growth temperature on material and device properties of thermally evaporated SnS thin-films and test structures. Grain size, Hall mobility, and majority-carrier concentration monotonically increase with growth temperature. However, the charge collection as measured by the long-wavelength contribution to short-circuit current exhibits a non-monotonic behavior: the collection decreases with increased growth temperature from 150 °C to 240 °C and then recovers at 285 °C. Fits to the experimental internal quantum efficiency using an opto-electronic model indicate that the non-monotonic behavior of charge-carrier collection can be explained by a transition from drift- to diffusion-assisted components of carrier collection. The results show a promising increase in the extracted minority-carrier diffusion length at the highest growth temperature of 285 °C. These findings illustrate how coupled mechanisms can affect early stage device development, highlighting the critical role of direct materials property measurements and simulation

  11. Application of Hybrid Genetic Algorithm Routine in Optimizing Food and Bioengineering Processes

    Directory of Open Access Journals (Sweden)

    Jaya Shankar Tumuluru

    2016-11-01

    Full Text Available Optimization is a crucial step in the analysis of experimental results. Deterministic methods only converge on local optimums and require exponentially more time as dimensionality increases. Stochastic algorithms are capable of efficiently searching the domain space; however convergence is not guaranteed. This article demonstrates the novelty of the hybrid genetic algorithm (HGA, which combines both stochastic and deterministic routines for improved optimization results. The new hybrid genetic algorithm developed is applied to the Ackley benchmark function as well as case studies in food, biofuel, and biotechnology processes. For each case study, the hybrid genetic algorithm found a better optimum candidate than reported by the sources. In the case of food processing, the hybrid genetic algorithm improved the anthocyanin yield by 6.44%. Optimization of bio-oil production using HGA resulted in a 5.06% higher yield. In the enzyme production process, HGA predicted a 0.39% higher xylanase yield. Hybridization of the genetic algorithm with a deterministic algorithm resulted in an improved optimum compared to statistical methods.

  12. A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation.

    Science.gov (United States)

    Pelet, S; Previte, M J R; Laiho, L H; So, P T C

    2004-10-01

    Global fitting algorithms have been shown to improve effectively the accuracy and precision of the analysis of fluorescence lifetime imaging microscopy data. Global analysis performs better than unconstrained data fitting when prior information exists, such as the spatial invariance of the lifetimes of individual fluorescent species. The highly coupled nature of global analysis often results in a significantly slower convergence of the data fitting algorithm as compared with unconstrained analysis. Convergence speed can be greatly accelerated by providing appropriate initial guesses. Realizing that the image morphology often correlates with fluorophore distribution, a global fitting algorithm has been developed to assign initial guesses throughout an image based on a segmentation analysis. This algorithm was tested on both simulated data sets and time-domain lifetime measurements. We have successfully measured fluorophore distribution in fibroblasts stained with Hoechst and calcein. This method further allows second harmonic generation from collagen and elastin autofluorescence to be differentiated in fluorescence lifetime imaging microscopy images of ex vivo human skin. On our experimental measurement, this algorithm increased convergence speed by over two orders of magnitude and achieved significantly better fits. Copyright 2004 Biophysical Society

  13. The effect of the electrical double layer on hydrodynamic lubrication: a non-monotonic trend with increasing zeta potential

    Directory of Open Access Journals (Sweden)

    Dalei Jing

    2017-07-01

    Full Text Available In the present study, a modified Reynolds equation including the electrical double layer (EDL-induced electroviscous effect of lubricant is established to investigate the effect of the EDL on the hydrodynamic lubrication of a 1D slider bearing. The theoretical model is based on the nonlinear Poisson–Boltzmann equation without the use of the Debye–Hückel approximation. Furthermore, the variation in the bulk electrical conductivity of the lubricant under the influence of the EDL is also considered during the theoretical analysis of hydrodynamic lubrication. The results show that the EDL can increase the hydrodynamic load capacity of the lubricant in a 1D slider bearing. More importantly, the hydrodynamic load capacity of the lubricant under the influence of the EDL shows a non-monotonic trend, changing from enhancement to attenuation with a gradual increase in the absolute value of the zeta potential. This non-monotonic hydrodynamic lubrication is dependent on the non-monotonic electroviscous effect of the lubricant generated by the EDL, which is dominated by the non-monotonic electrical field strength and non-monotonic electrical body force on the lubricant. The subject of the paper is the theoretical modeling and the corresponding analysis.

  14. Sparse Variational Bayesian SAGE Algorithm With Application to the Estimation of Multipath Wireless Channels

    DEFF Research Database (Denmark)

    Shutin, Dmitriy; Fleury, Bernard Henri

    2011-01-01

    In this paper, we develop a sparse variational Bayesian (VB) extension of the space-alternating generalized expectation-maximization (SAGE) algorithm for the high resolution estimation of the parameters of relevant multipath components in the response of frequency and spatially selective wireless...... channels. The application context of the algorithm considered in this contribution is parameter estimation from channel sounding measurements for radio channel modeling purpose. The new sparse VB-SAGE algorithm extends the classical SAGE algorithm in two respects: i) by monotonically minimizing...... parametric sparsity priors for the weights of the multipath components. We revisit the Gaussian sparsity priors within the sparse VB-SAGE framework and extend the results by considering Laplace priors. The structure of the VB-SAGE algorithm allows for an analytical stability analysis of the update expression...

  15. Modelling the drained response of bucket foundations for offshore wind turbines under general monotonic and cyclic loading

    DEFF Research Database (Denmark)

    Foglia, Aligi; Gottardi, Guido; Govoni, Laura

    2015-01-01

    The response of bucket foundations on sand subjected to planar monotonic and cyclic loading is investigated in the paper. Thirteen monotonic and cyclic laboratory tests on a skirted footing model having a 0.3 m diameter and embedment ratio equal to 1 are presented. The loading regime reproduces t...

  16. Multigenerational contaminant exposures produce non-monotonic, transgenerational responses in Daphnia magna

    International Nuclear Information System (INIS)

    Kimberly, David A.; Salice, Christopher J.

    2015-01-01

    Generally, ecotoxicologists rely on short-term tests that assume populations to be static. Conversely, natural populations may be exposed to the same stressors for many generations, which can alter tolerance to the same (or other) stressors. The objective of this study was to improve our understanding of how multigenerational stressors alter life history traits and stressor tolerance. After continuously exposing Daphnia magna to cadmium for 120 days, we assessed life history traits and conducted a challenge at higher temperature and cadmium concentrations. Predictably, individuals exposed to cadmium showed an overall decrease in reproductive output compared to controls. Interestingly, control D. magna were the most cadmium tolerant to novel cadmium, followed by those exposed to high cadmium. Our data suggest that long-term exposure to cadmium alter tolerance traits in a non-monotonic way. Because we observed effects after one-generation removal from cadmium, transgenerational effects may be possible as a result of multigenerational exposure. - Highlights: • Daphnia magna exposed to cadmium for 120 days. • D. magna exposed to cadmium had decreased reproductive output. • Control D. magna were most cadmium tolerant to novel cadmium stress. • Long-term exposure to cadmium alter tolerance traits in a non-monotonic way. • Transgenerational effects observed as a result of multigenerational exposure. - Adverse effects of long-term cadmium exposure persist into cadmium free conditions, as seen by non-monotonic responses when exposed to novel stress one generation removed.

  17. Efficient Actor-Critic Algorithm with Hierarchical Model Learning and Planning

    Science.gov (United States)

    Fu, QiMing

    2016-01-01

    To improve the convergence rate and the sample efficiency, two efficient learning methods AC-HMLP and RAC-HMLP (AC-HMLP with ℓ 2-regularization) are proposed by combining actor-critic algorithm with hierarchical model learning and planning. The hierarchical models consisting of the local and the global models, which are learned at the same time during learning of the value function and the policy, are approximated by local linear regression (LLR) and linear function approximation (LFA), respectively. Both the local model and the global model are applied to generate samples for planning; the former is used only if the state-prediction error does not surpass the threshold at each time step, while the latter is utilized at the end of each episode. The purpose of taking both models is to improve the sample efficiency and accelerate the convergence rate of the whole algorithm through fully utilizing the local and global information. Experimentally, AC-HMLP and RAC-HMLP are compared with three representative algorithms on two Reinforcement Learning (RL) benchmark problems. The results demonstrate that they perform best in terms of convergence rate and sample efficiency. PMID:27795704

  18. Multiscale high-order/low-order (HOLO) algorithms and applications

    International Nuclear Information System (INIS)

    Chacón, L.; Chen, G.; Knoll, D.A.; Newman, C.; Park, H.; Taitano, W.; Willert, J.A.; Womeldorff, G.

    2017-01-01

    We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

  19. Multiscale high-order/low-order (HOLO) algorithms and applications

    Energy Technology Data Exchange (ETDEWEB)

    Chacón, L., E-mail: chacon@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Chen, G.; Knoll, D.A.; Newman, C.; Park, H.; Taitano, W. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Willert, J.A. [Institute for Defense Analyses, Alexandria, VA 22311 (United States); Womeldorff, G. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

    2017-02-01

    We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

  20. A Direct Search Algorithm for Global Optimization

    Directory of Open Access Journals (Sweden)

    Enrique Baeyens

    2016-06-01

    Full Text Available A direct search algorithm is proposed for minimizing an arbitrary real valued function. The algorithm uses a new function transformation and three simplex-based operations. The function transformation provides global exploration features, while the simplex-based operations guarantees the termination of the algorithm and provides global convergence to a stationary point if the cost function is differentiable and its gradient is Lipschitz continuous. The algorithm’s performance has been extensively tested using benchmark functions and compared to some well-known global optimization algorithms. The results of the computational study show that the algorithm combines both simplicity and efficiency and is competitive with the heuristics-based strategies presently used for global optimization.

  1. Convergence

    Science.gov (United States)

    Darcie, Thomas E.; Doverspike, Robert; Zirngibl, Martin; Korotky, Steven K.

    2005-01-01

    .p {padding-bottom:6px} Call for Papers: Convergence Guest Editors: Thomas E. Darcie, University of Victoria Robert Doverspike, AT&T Martin Zirngibl, Lucent Technologies Coordinating Associate Editor: Steven K. Korotky, Lucent Technologies The Journal of Optical Networking (JON) invites submissions to a special issue on Convergence. Convergence has become a popular theme in telecommunications, one that has broad implications across all segments of the industry. Continual evolution of technology and applications continues to erase lines between traditionally separate lines of business, with dramatic consequences for vendors, service providers, and consumers. Spectacular advances in all layers of optical networking-leading to abundant, dynamic, cost-effective, and reliable wide-area and local-area connections-have been essential drivers of this evolution. As services and networks continue to evolve towards some notion of convergence, the continued role of optical networks must be explored. One vision of convergence renders all information in a common packet (especially IP) format. This vision is driven by the proliferation of data services. For example, time-division multiplexed (TDM) voice becomes VoIP. Analog cable-television signals become MPEG bits streamed to digital set-top boxes. T1 or OC-N private lines migrate to Ethernet virtual private networks (VPNs). All these packets coexist peacefully within a single packet-routing methodology built on an optical transport layer that combines the flexibility and cost of data networks with telecom-grade reliability. While this vision is appealing in its simplicity and shared widely, specifics of implementation raise many challenges and differences of opinion. For example, many seek to expand the role of Ethernet in these transport networks, while massive efforts are underway to make traditional TDM networks more data friendly within an evolved but backward-compatible SDH/SONET (synchronous digital hierarchy and

  2. Convergence

    Science.gov (United States)

    Darcie, Thomas E.; Doverspike, Robert; Zirngibl, Martin; Korotky, Steven K.

    2005-09-01

    Call for Papers: Convergence The Journal of Optical Networking (JON) invites submissions to a special issue on Convergence. Convergence has become a popular theme in telecommunications, one that has broad implications across all segments of the industry. Continual evolution of technology and applications continues to erase lines between traditionally separate lines of business, with dramatic consequences for vendors, service providers, and consumers. Spectacular advances in all layers of optical networking-leading to abundant, dynamic, cost-effective, and reliable wide-area and local-area connections-have been essential drivers of this evolution. As services and networks continue to evolve towards some notion of convergence, the continued role of optical networks must be explored. One vision of convergence renders all information in a common packet (especially IP) format. This vision is driven by the proliferation of data services. For example, time-division multiplexed (TDM) voice becomes VoIP. Analog cable-television signals become MPEG bits streamed to digital set-top boxes. T1 or OC-N private lines migrate to Ethernet virtual private networks (VPNs). All these packets coexist peacefully within a single packet-routing methodology built on an optical transport layer that combines the flexibility and cost of data networks with telecom-grade reliability. While this vision is appealing in its simplicity and shared widely, specifics of implementation raise many challenges and differences of opinion. For example, many seek to expand the role of Ethernet in these transport networks, while massive efforts are underway to make traditional TDM networks more data friendly within an evolved but backward-compatible SDH/SONET (synchronous digital hierarchy and synchronous optical network) multiplexing hierarchy. From this common underlying theme follow many specific instantiations. Examples include the convergence at the physical, logical, and operational levels of voice and

  3. An Ameliorative Whale Optimization Algorithm for Multi-Objective Optimal Allocation of Water Resources in Handan, China

    Directory of Open Access Journals (Sweden)

    Zhihong Yan

    2018-01-01

    Full Text Available With the deepening discrepancy between water supply and demand caused by water shortages, alleviating water shortages by optimizing water resource allocation has received extensive attention. How to allocate water resources optimally, rapidly, and effectively has become a challenging problem. Thus, this study employs a meta-heuristic swarm-based algorithm, the whale optimization algorithm (WOA. To overcome drawbacks like relatively low convergence precision and convergence rates, when applying the WOA algorithm to complex optimization problems, logistic mapping is used to initialize swarm location, and inertia weighting is employed to improve the algorithm. The resulting ameliorative whale optimization algorithm (AWOA shows substantially enhanced convergence rates and precision than the WOA and particle swarm optimization algorithms, demonstrating relatively high reliability and applicability. A water resource allocation optimization model with optimal economic efficiency and least total water shortage volume is established for Handan, China, and solved by the AWOA. The allocation results better reflect actual water usage in Handan. In 2030, the p = 50% total water shortage is forecast as 404.34 × 106 m3 or 14.8%. The shortage is mainly in the primary agricultural sector. The allocation results provide a reference for regional water resources management.

  4. Experimental quantum control landscapes: Inherent monotonicity and artificial structure

    International Nuclear Information System (INIS)

    Roslund, Jonathan; Rabitz, Herschel

    2009-01-01

    Unconstrained searches over quantum control landscapes are theoretically predicted to generally exhibit trap-free monotonic behavior. This paper makes an explicit experimental demonstration of this intrinsic monotonicity for two controlled quantum systems: frequency unfiltered and filtered second-harmonic generation (SHG). For unfiltered SHG, the landscape is randomly sampled and interpolation of the data is found to be devoid of landscape traps up to the level of data noise. In the case of narrow-band-filtered SHG, trajectories are taken on the landscape to reveal a lack of traps. Although the filtered SHG landscape is trap free, it exhibits a rich local structure. A perturbation analysis around the top of these landscapes provides a basis to understand their topology. Despite the inherent trap-free nature of the landscapes, practical constraints placed on the controls can lead to the appearance of artificial structure arising from the resultant forced sampling of the landscape. This circumstance and the likely lack of knowledge about the detailed local landscape structure in most quantum control applications suggests that the a priori identification of globally successful (un)constrained curvilinear control variables may be a challenging task.

  5. A Parallel Adaptive Particle Swarm Optimization Algorithm for Economic/Environmental Power Dispatch

    Directory of Open Access Journals (Sweden)

    Jinchao Li

    2012-01-01

    Full Text Available A parallel adaptive particle swarm optimization algorithm (PAPSO is proposed for economic/environmental power dispatch, which can overcome the premature characteristic, the slow-speed convergence in the late evolutionary phase, and lacking good direction in particles’ evolutionary process. A search population is randomly divided into several subpopulations. Then for each subpopulation, the optimal solution is searched synchronously using the proposed method, and thus parallel computing is realized. To avoid converging to a local optimum, a crossover operator is introduced to exchange the information among the subpopulations and the diversity of population is sustained simultaneously. Simulation results show that the proposed algorithm can effectively solve the economic/environmental operation problem of hydropower generating units. Performance comparisons show that the solution from the proposed method is better than those from the conventional particle swarm algorithm and other optimization algorithms.

  6. ANALYSIS OF CONVERGENCE WITHIN THE EUROPEAN UNION SIGMA AND BETA CONVERGENCE

    Directory of Open Access Journals (Sweden)

    Begu Liviu-Stelian

    2010-12-01

    Full Text Available Real convergence study began with the development of neoclassical models of growth and especially with the passage of econometric applications of these models. In this paper we present applications of indicators and patterns of convergence on the example of European Union member countries and some current economic impact assessments on European convergence process. This analysis is based on the estimated a- and b convergence and on Markov chains. The study deals with the economic convergence of the European countries and especially the convergence of the EU countries, including Romania. In the end of the study presents several economic scenarios for a faster and easier exit from the current crisis in Romania.

  7. Data classification using metaheuristic Cuckoo Search technique for Levenberg Marquardt back propagation (CSLM) algorithm

    Science.gov (United States)

    Nawi, Nazri Mohd.; Khan, Abdullah; Rehman, M. Z.

    2015-05-01

    A nature inspired behavior metaheuristic techniques which provide derivative-free solutions to solve complex problems. One of the latest additions to the group of nature inspired optimization procedure is Cuckoo Search (CS) algorithm. Artificial Neural Network (ANN) training is an optimization task since it is desired to find optimal weight set of a neural network in training process. Traditional training algorithms have some limitation such as getting trapped in local minima and slow convergence rate. This study proposed a new technique CSLM by combining the best features of two known algorithms back-propagation (BP) and Levenberg Marquardt algorithm (LM) for improving the convergence speed of ANN training and avoiding local minima problem by training this network. Some selected benchmark classification datasets are used for simulation. The experiment result show that the proposed cuckoo search with Levenberg Marquardt algorithm has better performance than other algorithm used in this study.

  8. Finite time convergent learning law for continuous neural networks.

    Science.gov (United States)

    Chairez, Isaac

    2014-02-01

    This paper addresses the design of a discontinuous finite time convergent learning law for neural networks with continuous dynamics. The neural network was used here to obtain a non-parametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties was the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on discontinuous algorithms was used to adjust the weights of the neural network. The adaptive algorithm was derived by means of a non-standard Lyapunov function that is lower semi-continuous and differentiable in almost the whole space. A compensator term was included in the identifier to reject some specific perturbations using a nonlinear robust algorithm. Two numerical examples demonstrated the improvements achieved by the learning algorithm introduced in this paper compared to classical schemes with continuous learning methods. The first one dealt with a benchmark problem used in the paper to explain how the discontinuous learning law works. The second one used the methane production model to show the benefits in engineering applications of the learning law proposed in this paper. Copyright © 2013 Elsevier Ltd. All rights reserved.

  9. Quantitative non-monotonic modeling of economic uncertainty by probability and possibility distributions

    DEFF Research Database (Denmark)

    Schjær-Jacobsen, Hans

    2012-01-01

    uncertainty can be calculated. The possibility approach is particular well suited for representation of uncertainty of a non-statistical nature due to lack of knowledge and requires less information than the probability approach. Based on the kind of uncertainty and knowledge present, these aspects...... to the understanding of similarities and differences of the two approaches as well as practical applications. The probability approach offers a good framework for representation of randomness and variability. Once the probability distributions of uncertain parameters and their correlations are known the resulting...... are thoroughly discussed in the case of rectangular representation of uncertainty by the uniform probability distribution and the interval, respectively. Also triangular representations are dealt with and compared. Calculation of monotonic as well as non-monotonic functions of variables represented...

  10. Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients

    KAUST Repository

    Matevosyan, Norayr; Petrosyan, Arshak

    2010-01-01

    In this paper we extend the results of Caffarelli, Jerison, and Kenig [Ann. of Math. (2)155 (2002)] and Caffarelli and Kenig [Amer. J. Math.120 (1998)] by establishing an almost monotonicity estimate for pairs of continuous functions satisfying u

  11. Non-monotonic reasoning in conceptual modeling and ontology design: A proposal

    CSIR Research Space (South Africa)

    Casini, G

    2013-06-01

    Full Text Available -1 2nd International Workshop on Ontologies and Conceptual Modeling (Onto.Com 2013), Valencia, Spain, 17-21 June 2013 Non-monotonic reasoning in conceptual modeling and ontology design: A proposal Giovanni Casini1 and Alessandro Mosca2 1...

  12. Convergence of iterative image reconstruction algorithms for Digital Breast Tomosynthesis

    DEFF Research Database (Denmark)

    Sidky, Emil; Jørgensen, Jakob Heide; Pan, Xiaochuan

    2012-01-01

    Most iterative image reconstruction algorithms are based on some form of optimization, such as minimization of a data-fidelity term plus an image regularizing penalty term. While achieving the solution of these optimization problems may not directly be clinically relevant, accurate optimization s...

  13. High-Dimensional Exploratory Item Factor Analysis by a Metropolis-Hastings Robbins-Monro Algorithm

    Science.gov (United States)

    Cai, Li

    2010-01-01

    A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The…

  14. Estimation of Poisson-Dirichlet Parameters with Monotone Missing Data

    Directory of Open Access Journals (Sweden)

    Xueqin Zhou

    2017-01-01

    Full Text Available This article considers the estimation of the unknown numerical parameters and the density of the base measure in a Poisson-Dirichlet process prior with grouped monotone missing data. The numerical parameters are estimated by the method of maximum likelihood estimates and the density function is estimated by kernel method. A set of simulations was conducted, which shows that the estimates perform well.

  15. Monotonous braking of high energy hadrons in nuclear matter

    International Nuclear Information System (INIS)

    Strugalski, Z.

    1979-01-01

    Propagation of high energy hadrons in nuclear matter is discussed. The possibility of the existence of the monotonous energy losses of hadrons in nuclear matter is considered. In favour of this hypothesis experimental facts such as pion-nucleus interactions (proton emission spectra, proton multiplicity distributions in these interactions) and other data are presented. The investigated phenomenon in the framework of the hypothesis is characterized in more detail

  16. Algorithms for parallel computers

    International Nuclear Information System (INIS)

    Churchhouse, R.F.

    1985-01-01

    Until relatively recently almost all the algorithms for use on computers had been designed on the (usually unstated) assumption that they were to be run on single processor, serial machines. With the introduction of vector processors, array processors and interconnected systems of mainframes, minis and micros, however, various forms of parallelism have become available. The advantage of parallelism is that it offers increased overall processing speed but it also raises some fundamental questions, including: (i) which, if any, of the existing 'serial' algorithms can be adapted for use in the parallel mode. (ii) How close to optimal can such adapted algorithms be and, where relevant, what are the convergence criteria. (iii) How can we design new algorithms specifically for parallel systems. (iv) For multi-processor systems how can we handle the software aspects of the interprocessor communications. Aspects of these questions illustrated by examples are considered in these lectures. (orig.)

  17. Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

    Directory of Open Access Journals (Sweden)

    Xisheng Yu

    2014-01-01

    Full Text Available The paper by Liu (2010 introduces a method termed the canonical least-squares Monte Carlo (CLM which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.

  18. Science and technology convergence: with emphasis for nanotechnology-inspired convergence

    Energy Technology Data Exchange (ETDEWEB)

    Bainbridge, William S.; Roco, Mihail C., E-mail: mroco@nsf.gov [National Science Foundation (United States)

    2016-07-15

    Convergence offers a new universe of discovery, innovation, and application opportunities through specific theories, principles, and methods to be implemented in research, education, production, and other societal activities. Using a holistic approach with shared goals, convergence seeks to transcend existing human limitations to achieve improved conditions for work, learning, aging, physical, and cognitive wellness. This paper outlines ten key theories that offer complementary perspectives on this complex dynamic. Principles and methods are proposed to facilitate and enhance science and technology convergence. Several convergence success stories in the first part of the 21st century—including nanotechnology and other emerging technologies—are discussed in parallel with case studies focused on the future. The formulation of relevant theories, principles, and methods aims at establishing the convergence science.

  19. Science and technology convergence: with emphasis for nanotechnology-inspired convergence

    International Nuclear Information System (INIS)

    Bainbridge, William S.; Roco, Mihail C.

    2016-01-01

    Convergence offers a new universe of discovery, innovation, and application opportunities through specific theories, principles, and methods to be implemented in research, education, production, and other societal activities. Using a holistic approach with shared goals, convergence seeks to transcend existing human limitations to achieve improved conditions for work, learning, aging, physical, and cognitive wellness. This paper outlines ten key theories that offer complementary perspectives on this complex dynamic. Principles and methods are proposed to facilitate and enhance science and technology convergence. Several convergence success stories in the first part of the 21st century—including nanotechnology and other emerging technologies—are discussed in parallel with case studies focused on the future. The formulation of relevant theories, principles, and methods aims at establishing the convergence science.

  20. Quantisation of monotonic twist maps

    International Nuclear Information System (INIS)

    Boasman, P.A.; Smilansky, U.

    1993-08-01

    Using an approach suggested by Moser, classical Hamiltonians are generated that provide an interpolating flow to the stroboscopic motion of maps with a monotonic twist condition. The quantum properties of these Hamiltonians are then studied in analogy with recent work on the semiclassical quantization of systems based on Poincare surfaces of section. For the generalized standard map, the correspondence with the usual classical and quantum results is shown, and the advantages of the quantum Moser Hamiltonian demonstrated. The same approach is then applied to the free motion of a particle on a 2-torus, and to the circle billiard. A natural quantization condition based on the eigenphases of the unitary time--development operator is applied, leaving the exact eigenvalues of the torus, but only the semiclassical eigenvalues for the billiard; an explanation for this failure is proposed. It is also seen how iterating the classical map commutes with the quantization. (authors)

  1. Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

    Directory of Open Access Journals (Sweden)

    Zakieh Avazzadeh

    2014-01-01

    Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

  2. The Medusa Algorithm for Polynomial Matings

    DEFF Research Database (Denmark)

    Boyd, Suzanne Hruska; Henriksen, Christian

    2012-01-01

    of its Julia set. Whether these approximations converge is answered using Thurston's topological characterization of rational maps. This algorithm was designed by John Hamal Hubbard, and implemented in 1998 by Christian Henriksen and REU students David Farris and Kuon Ju Liu. In this paper we describe...

  3. A modified 4D ROOSTER method using the Chambolle-Pock algorithm

    OpenAIRE

    Mory, Cyril; Jacques, Laurent; The Third International Conference on Image Formation in X-Ray Computed Tomography

    2014-01-01

    The 4D RecOnstructiOn using Spatial and TEmpo- ral Regularization method is a recent 4D cone beam computed tomography algorithm. 4D ROOSTER has not been rigorously proved to converge. This paper aims to reformulate it using the Chambolle & Pock primal-dual optimization scheme. The convergence of this reformulated 4D ROOSTER is therefore guaranteed.

  4. Simultaneous and semi-alternating projection algorithms for solving split equality problems.

    Science.gov (United States)

    Dong, Qiao-Li; Jiang, Dan

    2018-01-01

    In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms.

  5. Convergence analysis of particle swarm optimization (PSO) method on the with-in host dengue infection treatment model

    Science.gov (United States)

    Handayani, D.; Nuraini, N.; Tse, O.; Saragih, R.; Naiborhu, J.

    2016-04-01

    PSO is a computational optimization method motivated by the social behavior of organisms like bird flocking, fish schooling and human social relations. PSO is one of the most important swarm intelligence algorithms. In this study, we analyze the convergence of PSO when it is applied to with-in host dengue infection treatment model simulation in our early research. We used PSO method to construct the initial adjoin equation and to solve a control problem. Its properties of control input on the continuity of objective function and ability of adapting to the dynamic environment made us have to analyze the convergence of PSO. With the convergence analysis of PSO we will have some parameters that ensure the convergence result of numerical simulations on this model using PSO.

  6. IT-BT convergence technology

    International Nuclear Information System (INIS)

    2012-12-01

    This book explains IT-BT convergence technology as the future technology, which includes a prolog, easy IT-BT convergence technology that has infinite potentials for new value, policy of IT-BT convergence technology showing the potential of smart Korea, IT-BT convergence opening happy future, for the new future of IT powerful nation Korea with IT-BT convergence technology and an epilogue. This book reveals the conception, policy, performance and future of IT-BT convergence technology.

  7. Performance study of LMS based adaptive algorithms for unknown system identification

    Energy Technology Data Exchange (ETDEWEB)

    Javed, Shazia; Ahmad, Noor Atinah [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang (Malaysia)

    2014-07-10

    Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment.

  8. Performance study of LMS based adaptive algorithms for unknown system identification

    International Nuclear Information System (INIS)

    Javed, Shazia; Ahmad, Noor Atinah

    2014-01-01

    Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment

  9. Algorithms for the optimization of RBE-weighted dose in particle therapy.

    Science.gov (United States)

    Horcicka, M; Meyer, C; Buschbacher, A; Durante, M; Krämer, M

    2013-01-21

    We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

  10. Convergence analysis of a class of massively parallel direction splitting algorithms for the Navier-Stokes equations in simple domains

    KAUST Repository

    Guermond, Jean-Luc; Minev, Peter D.; Salgado, Abner J.

    2012-01-01

    We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.

  11. A CLASS OF NONMONOTONE TRUST REGION ALGORITHMS FOR LINEARLY CONSTRAINED OPTIMIZATION%线性约束优化的一类非单调信赖域算法

    Institute of Scientific and Technical Information of China (English)

    葛恒武; 陈中文

    2002-01-01

    We present a class of nonmonotone trust region algorithms for linearly constrained optimization in this paper.The algorithm may adjust automatically the scope of the monotonicity by the degree that the quadratic model is "trusted".Under the suitable conditions,it is proved that any limit point of the infinite sequence generated by the algorithm is the Kuhn-Tucker point of the primal problem.Finally,some numerical results show that the new algorithm is very effective.

  12. Convergence in Multispecies Interactions

    OpenAIRE

    Bittleston, Leonora Sophia; Pierce, Naomi E.; Ellison, Aaron M.; Pringle, Anne

    2016-01-01

    The concepts of convergent evolution and community convergence highlight how selective pressures can shape unrelated organisms or communities in similar ways. We propose a related concept, convergent interactions, to describe the independent evolution of multispecies interactions with similar physiological or ecological functions. A focus on convergent interactions clarifies how natural selection repeatedly favors particular kinds of associations among species. Characterizing convergent inter...

  13. Monotonous property of non-oscillations of the damped Duffing's equation

    International Nuclear Information System (INIS)

    Feng Zhaosheng

    2006-01-01

    In this paper, we give a qualitative study to the damped Duffing's equation by means of the qualitative theory of planar systems. Under certain parametric conditions, the monotonous property of the bounded non-oscillations is obtained. Explicit exact solutions are obtained by a direct method and application of this approach to a reaction-diffusion equation is presented

  14. Monotonicity and Logarithmic Concavity of Two Functions Involving Exponential Function

    Science.gov (United States)

    Liu, Ai-Qi; Li, Guo-Fu; Guo, Bai-Ni; Qi, Feng

    2008-01-01

    The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…

  15. On monotonic solutions of an integral equation of Abel type

    International Nuclear Information System (INIS)

    Darwish, Mohamed Abdalla

    2007-08-01

    We present an existence theorem of monotonic solutions for a quadratic integral equation of Abel type in C[0, 1]. The famous Chandrasekhar's integral equation is considered as a special case. The concept of measure of noncompactness and a fi xed point theorem due to Darbo are the main tools in carrying out our proof. (author)

  16. A homogeneous interior-point algorithm for nonsymmetric convex conic optimization

    DEFF Research Database (Denmark)

    Skajaa, Anders; Ye, Yinyu

    2014-01-01

    -centered primal–dual point. Features of the algorithm include that it makes use only of the primal barrier function, that it is able to detect infeasibilities in the problem and that no phase-I method is needed. We prove convergence to TeX -accuracy in TeX iterations. To improve performance, the algorithm employs...

  17. Convergent cross-mapping and pairwise asymmetric inference.

    Science.gov (United States)

    McCracken, James M; Weigel, Robert S

    2014-12-01

    Convergent cross-mapping (CCM) is a technique for computing specific kinds of correlations between sets of times series. It was introduced by Sugihara et al. [Science 338, 496 (2012).] and is reported to be "a necessary condition for causation" capable of distinguishing causality from standard correlation. We show that the relationships between CCM correlations proposed by Sugihara et al. do not, in general, agree with intuitive concepts of "driving" and as such should not be considered indicative of causality. It is shown that the fact that the CCM algorithm implies causality is a function of system parameters for simple linear and nonlinear systems. For example, in a circuit containing a single resistor and inductor, both voltage and current can be identified as the driver depending on the frequency of the source voltage. It is shown that the CCM algorithm, however, can be modified to identify relationships between pairs of time series that are consistent with intuition for the considered example systems for which CCM causality analysis provided nonintuitive driver identifications. This modification of the CCM algorithm is introduced as "pairwise asymmetric inference" (PAI) and examples of its use are presented.

  18. An error bound estimate and convergence of the Nodal-LTS N solution in a rectangle

    International Nuclear Information System (INIS)

    Hauser, Eliete Biasotto; Pazos, Ruben Panta; Tullio de Vilhena, Marco

    2005-01-01

    In this work, we report the mathematical analysis concerning error bound estimate and convergence of the Nodal-LTS N solution in a rectangle. For such we present an efficient algorithm, called LTS N 2D-Diag solution for Cartesian geometry

  19. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

  20. Hemiequilibrium problems

    Directory of Open Access Journals (Sweden)

    Muhammad Aslam Noor

    2004-01-01

    Full Text Available We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new method for hemivariational inequalities. Since hemiequilibrium problems include hemivariational inequalities and equilibrium problems as special cases, the results proved in this paper still hold for these problems.

  1. Coupled reaction-diffusion equations to model the fission gas release in the irradiation of the uranium dioxide

    International Nuclear Information System (INIS)

    Moyano, Edgardo A.; Scarpettini, Alberto F.

    2003-01-01

    A semi linear model of weakly coupled parabolic p.d.e. with reaction-diffusion is investigated. The system describes fission gas transfer from grain interior of UO 2 to grain boundaries. The problem is studied in a bounded domain. Using the upper-lower solutions method, two monotone sequences for the finite differences equations are constructed. Reasons are mentioned that allow to affirm that in the proposed functional sector the algorithm converges to the unique solution of the differential system. (author)

  2. Optimal configuration of power grid sources based on optimal particle swarm algorithm

    Science.gov (United States)

    Wen, Yuanhua

    2018-04-01

    In order to optimize the distribution problem of power grid sources, an optimized particle swarm optimization algorithm is proposed. First, the concept of multi-objective optimization and the Pareto solution set are enumerated. Then, the performance of the classical genetic algorithm, the classical particle swarm optimization algorithm and the improved particle swarm optimization algorithm are analyzed. The three algorithms are simulated respectively. Compared with the test results of each algorithm, the superiority of the algorithm in convergence and optimization performance is proved, which lays the foundation for subsequent micro-grid power optimization configuration solution.

  3. Logarithmically complete monotonicity of a function related to the Catalan-Qi function

    Directory of Open Access Journals (Sweden)

    Qi Feng

    2016-08-01

    Full Text Available In the paper, the authors find necessary and sufficient conditions such that a function related to the Catalan-Qi function, which is an alternative generalization of the Catalan numbers, is logarithmically complete monotonic.

  4. A note on profit maximization and monotonicity for inbound call centers

    NARCIS (Netherlands)

    Koole, G.M.; Pot, S.A.

    2011-01-01

    We consider an inbound call center with a fixed reward per call and communication and agent costs. By controlling the number of lines and the number of agents, we can maximize the profit. Abandonments are included in our performance model. Monotonicity results for the maximization problem are

  5. Fast parallel MR image reconstruction via B1-based, adaptive restart, iterative soft thresholding algorithms (BARISTA).

    Science.gov (United States)

    Muckley, Matthew J; Noll, Douglas C; Fessler, Jeffrey A

    2015-02-01

    Sparsity-promoting regularization is useful for combining compressed sensing assumptions with parallel MRI for reducing scan time while preserving image quality. Variable splitting algorithms are the current state-of-the-art algorithms for SENSE-type MR image reconstruction with sparsity-promoting regularization. These methods are very general and have been observed to work with almost any regularizer; however, the tuning of associated convergence parameters is a commonly-cited hindrance in their adoption. Conversely, majorize-minimize algorithms based on a single Lipschitz constant have been observed to be slow in shift-variant applications such as SENSE-type MR image reconstruction since the associated Lipschitz constants are loose bounds for the shift-variant behavior. This paper bridges the gap between the Lipschitz constant and the shift-variant aspects of SENSE-type MR imaging by introducing majorizing matrices in the range of the regularizer matrix. The proposed majorize-minimize methods (called BARISTA) converge faster than state-of-the-art variable splitting algorithms when combined with momentum acceleration and adaptive momentum restarting. Furthermore, the tuning parameters associated with the proposed methods are unitless convergence tolerances that are easier to choose than the constraint penalty parameters required by variable splitting algorithms.

  6. Self-adaptive global best harmony search algorithm applied to reactor core fuel management optimization

    International Nuclear Information System (INIS)

    Poursalehi, N.; Zolfaghari, A.; Minuchehr, A.; Valavi, K.

    2013-01-01

    Highlights: • SGHS enhanced the convergence rate of LPO using some improvements in comparison to basic HS and GHS. • SGHS optimization algorithm obtained averagely better fitness relative to basic HS and GHS algorithms. • Upshot of the SGHS implementation in the LPO reveals its flexibility, efficiency and reliability. - Abstract: The aim of this work is to apply the new developed optimization algorithm, Self-adaptive Global best Harmony Search (SGHS), for PWRs fuel management optimization. SGHS algorithm has some modifications in comparison with basic Harmony Search (HS) and Global-best Harmony Search (GHS) algorithms such as dynamically change of parameters. For the demonstration of SGHS ability to find an optimal configuration of fuel assemblies, basic Harmony Search (HS) and Global-best Harmony Search (GHS) algorithms also have been developed and investigated. For this purpose, Self-adaptive Global best Harmony Search Nodal Expansion package (SGHSNE) has been developed implementing HS, GHS and SGHS optimization algorithms for the fuel management operation of nuclear reactor cores. This package uses developed average current nodal expansion code which solves the multi group diffusion equation by employment of first and second orders of Nodal Expansion Method (NEM) for two dimensional, hexagonal and rectangular geometries, respectively, by one node per a FA. Loading pattern optimization was performed using SGHSNE package for some test cases to present the SGHS algorithm capability in converging to near optimal loading pattern. Results indicate that the convergence rate and reliability of the SGHS method are quite promising and practically, SGHS improves the quality of loading pattern optimization results relative to HS and GHS algorithms. As a result, it has the potential to be used in the other nuclear engineering optimization problems

  7. Estimation of a monotone percentile residual life function under random censorship.

    Science.gov (United States)

    Franco-Pereira, Alba M; de Uña-Álvarez, Jacobo

    2013-01-01

    In this paper, we introduce a new estimator of a percentile residual life function with censored data under a monotonicity constraint. Specifically, it is assumed that the percentile residual life is a decreasing function. This assumption is useful when estimating the percentile residual life of units, which degenerate with age. We establish a law of the iterated logarithm for the proposed estimator, and its n-equivalence to the unrestricted estimator. The asymptotic normal distribution of the estimator and its strong approximation to a Gaussian process are also established. We investigate the finite sample performance of the monotone estimator in an extensive simulation study. Finally, data from a clinical trial in primary biliary cirrhosis of the liver are analyzed with the proposed methods. One of the conclusions of our work is that the restricted estimator may be much more efficient than the unrestricted one. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. On the convergence of finite state mean-field games through Γ-convergence

    KAUST Repository

    Ferreira, Rita C.; Gomes, Diogo A.

    2014-01-01

    In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.

  9. On the convergence of finite state mean-field games through Γ-convergence

    KAUST Repository

    Ferreira, Rita C.

    2014-10-01

    In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.

  10. New Enhanced Artificial Bee Colony (JA-ABC5 Algorithm with Application for Reactive Power Optimization

    Directory of Open Access Journals (Sweden)

    Noorazliza Sulaiman

    2015-01-01

    Full Text Available The standard artificial bee colony (ABC algorithm involves exploration and exploitation processes which need to be balanced for enhanced performance. This paper proposes a new modified ABC algorithm named JA-ABC5 to enhance convergence speed and improve the ability to reach the global optimum by balancing exploration and exploitation processes. New stages have been proposed at the earlier stages of the algorithm to increase the exploitation process. Besides that, modified mutation equations have also been introduced in the employed and onlooker-bees phases to balance the two processes. The performance of JA-ABC5 has been analyzed on 27 commonly used benchmark functions and tested to optimize the reactive power optimization problem. The performance results have clearly shown that the newly proposed algorithm has outperformed other compared algorithms in terms of convergence speed and global optimum achievement.

  11. New enhanced artificial bee colony (JA-ABC5) algorithm with application for reactive power optimization.

    Science.gov (United States)

    Sulaiman, Noorazliza; Mohamad-Saleh, Junita; Abro, Abdul Ghani

    2015-01-01

    The standard artificial bee colony (ABC) algorithm involves exploration and exploitation processes which need to be balanced for enhanced performance. This paper proposes a new modified ABC algorithm named JA-ABC5 to enhance convergence speed and improve the ability to reach the global optimum by balancing exploration and exploitation processes. New stages have been proposed at the earlier stages of the algorithm to increase the exploitation process. Besides that, modified mutation equations have also been introduced in the employed and onlooker-bees phases to balance the two processes. The performance of JA-ABC5 has been analyzed on 27 commonly used benchmark functions and tested to optimize the reactive power optimization problem. The performance results have clearly shown that the newly proposed algorithm has outperformed other compared algorithms in terms of convergence speed and global optimum achievement.

  12. Application of the DMRG in two dimensions: a parallel tempering algorithm

    Science.gov (United States)

    Hu, Shijie; Zhao, Jize; Zhang, Xuefeng; Eggert, Sebastian

    The Density Matrix Renormalization Group (DMRG) is known to be a powerful algorithm for treating one-dimensional systems. When the DMRG is applied in two dimensions, however, the convergence becomes much less reliable and typically ''metastable states'' may appear, which are unfortunately quite robust even when keeping a very high number of DMRG states. To overcome this problem we have now successfully developed a parallel tempering DMRG algorithm. Similar to parallel tempering in quantum Monte Carlo, this algorithm allows the systematic switching of DMRG states between different model parameters, which is very efficient for solving convergence problems. Using this method we have figured out the phase diagram of the xxz model on the anisotropic triangular lattice which can be realized by hardcore bosons in optical lattices. SFB Transregio 49 of the Deutsche Forschungsgemeinschaft (DFG) and the Allianz fur Hochleistungsrechnen Rheinland-Pfalz (AHRP).

  13. Network Convergence

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Network Convergence. User is interested in application and content - not technical means of distribution. Boundaries between distribution channels fade out. Network convergence leads to seamless application and content solutions.

  14. Use of the preconditioned conjugate gradient algorithm as a generic solver for mixed-model equations in animal breeding applications.

    Science.gov (United States)

    Tsuruta, S; Misztal, I; Strandén, I

    2001-05-01

    Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is

  15. A new method for data assimilation: the back and forth nudging algorithm

    OpenAIRE

    Auroux , Didier; Blum , Jacques; Nodet , Maëlle

    2013-01-01

    International audience; In this paper, we propose an improvement to the Back and Forth Nudging algorithm for handling diffusion in the context of geophysical data assimilation. We detail the Diffusive Back and Forth Nudging algorithm, in which the sign of the diffusion term is changed in the backward integrations. We study the convergence of this algorithm, in particular for linear transport equations.

  16. Genetic Algorithm Optimizes Q-LAW Control Parameters

    Science.gov (United States)

    Lee, Seungwon; von Allmen, Paul; Petropoulos, Anastassios; Terrile, Richard

    2008-01-01

    A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto-optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution. Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.

  17. Theory and algorithms for solving large-scale numerical problems. Application to the management of electricity production

    International Nuclear Information System (INIS)

    Chiche, A.

    2012-01-01

    This manuscript deals with large-scale optimization problems, and more specifically with solving the electricity unit commitment problem arising at EDF. First, we focused on the augmented Lagrangian algorithm. The behavior of that algorithm on an infeasible convex quadratic optimization problem is analyzed. It is shown that the algorithm finds a point that satisfies the shifted constraints with the smallest possible shift in the sense of the Euclidean norm and that it minimizes the objective on the corresponding shifted constrained set. The convergence to such a point is realized at a global linear rate, which depends explicitly on the augmentation parameter. This suggests us a rule for determining the augmentation parameter to control the speed of convergence of the shifted constraint norm to zero. This rule has the advantage of generating bounded augmentation parameters even when the problem is infeasible. As a by-product, the algorithm computes the smallest translation in the Euclidean norm that makes the constraints feasible. Furthermore, this work provides solution methods for stochastic optimization industrial problems decomposed on a scenario tree, based on the progressive hedging algorithm introduced by [Rockafellar et Wets, 1991]. We also focus on the convergence of that algorithm. On the one hand, we offer a counter-example showing that the algorithm could diverge if its augmentation parameter is iteratively updated. On the other hand, we show how to recover the multipliers associated with the non-dualized constraints defined on the scenario tree from those associated with the corresponding constraints of the scenario subproblems. Their convergence is also analyzed for convex problems. The practical interest of theses solutions techniques is corroborated by numerical experiments performed on the electric production management problem. We apply the progressive hedging algorithm to a realistic industrial problem. More precisely, we solve the French medium

  18. A New Numerical Algorithm for Two-Point Boundary Value Problems

    OpenAIRE

    Guo, Lihua; Wu, Boying; Zhang, Dazhi

    2014-01-01

    We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that the n-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

  19. EDDA: An Efficient Distributed Data Replication Algorithm in VANETs.

    Science.gov (United States)

    Zhu, Junyu; Huang, Chuanhe; Fan, Xiying; Guo, Sipei; Fu, Bin

    2018-02-10

    Efficient data dissemination in vehicular ad hoc networks (VANETs) is a challenging issue due to the dynamic nature of the network. To improve the performance of data dissemination, we study distributed data replication algorithms in VANETs for exchanging information and computing in an arbitrarily-connected network of vehicle nodes. To achieve low dissemination delay and improve the network performance, we control the number of message copies that can be disseminated in the network and then propose an efficient distributed data replication algorithm (EDDA). The key idea is to let the data carrier distribute the data dissemination tasks to multiple nodes to speed up the dissemination process. We calculate the number of communication stages for the network to enter into a balanced status and show that the proposed distributed algorithm can converge to a consensus in a small number of communication stages. Most of the theoretical results described in this paper are to study the complexity of network convergence. The lower bound and upper bound are also provided in the analysis of the algorithm. Simulation results show that the proposed EDDA can efficiently disseminate messages to vehicles in a specific area with low dissemination delay and system overhead.

  20. EDDA: An Efficient Distributed Data Replication Algorithm in VANETs

    Science.gov (United States)

    Zhu, Junyu; Huang, Chuanhe; Fan, Xiying; Guo, Sipei; Fu, Bin

    2018-01-01

    Efficient data dissemination in vehicular ad hoc networks (VANETs) is a challenging issue due to the dynamic nature of the network. To improve the performance of data dissemination, we study distributed data replication algorithms in VANETs for exchanging information and computing in an arbitrarily-connected network of vehicle nodes. To achieve low dissemination delay and improve the network performance, we control the number of message copies that can be disseminated in the network and then propose an efficient distributed data replication algorithm (EDDA). The key idea is to let the data carrier distribute the data dissemination tasks to multiple nodes to speed up the dissemination process. We calculate the number of communication stages for the network to enter into a balanced status and show that the proposed distributed algorithm can converge to a consensus in a small number of communication stages. Most of the theoretical results described in this paper are to study the complexity of network convergence. The lower bound and upper bound are also provided in the analysis of the algorithm. Simulation results show that the proposed EDDA can efficiently disseminate messages to vehicles in a specific area with low dissemination delay and system overhead. PMID:29439443

  1. Effect of dynamic monotonic and cyclic loading on fracture behavior for Japanese carbon steel pipe STS410

    Energy Technology Data Exchange (ETDEWEB)

    Kinoshita, Kanji; Murayama, Kouichi; Ogata, Hiroyuki [and others

    1997-04-01

    The fracture behavior for Japanese carbon steel pipe STS410 was examined under dynamic monotonic and cyclic loading through a research program of International Piping Integrity Research Group (EPIRG-2), in order to evaluate the strength of pipe during the seismic event The tensile test and the fracture toughness test were conducted for base metal and TIG weld metal. Three base metal pipe specimens, 1,500mm in length and 6-inch diameter sch.120, were employed for a quasi-static monotonic, a dynamic monotonic and a dynamic cyclic loading pipe fracture tests. One weld joint pipe specimen was also employed for a dynamic cyclic loading test In the dynamic cyclic loading test, the displacement was controlled as applying the fully reversed load (R=-1). The pipe specimens with a circumferential through-wall crack were subjected four point bending load at 300C in air. Japanese STS410 carbon steel pipe material was found to have high toughness under dynamic loading condition through the CT fracture toughness test. As the results of pipe fracture tests, the maximum moment to pipe fracture under dynamic monotonic and cyclic loading condition, could be estimated by plastic collapse criterion and the effect of dynamic monotonic loading and cyclic loading was a little on the maximum moment to pipe fracture of the STS410 carbon steel pipe. The STS410 carbon steel pipe seemed to be less sensitive to dynamic and cyclic loading effects than the A106Gr.B carbon steel pipe evaluated in IPIRG-1 program.

  2. Effect of dynamic monotonic and cyclic loading on fracture behavior for Japanese carbon steel pipe STS410

    International Nuclear Information System (INIS)

    Kinoshita, Kanji; Murayama, Kouichi; Ogata, Hiroyuki

    1997-01-01

    The fracture behavior for Japanese carbon steel pipe STS410 was examined under dynamic monotonic and cyclic loading through a research program of International Piping Integrity Research Group (EPIRG-2), in order to evaluate the strength of pipe during the seismic event The tensile test and the fracture toughness test were conducted for base metal and TIG weld metal. Three base metal pipe specimens, 1,500mm in length and 6-inch diameter sch.120, were employed for a quasi-static monotonic, a dynamic monotonic and a dynamic cyclic loading pipe fracture tests. One weld joint pipe specimen was also employed for a dynamic cyclic loading test In the dynamic cyclic loading test, the displacement was controlled as applying the fully reversed load (R=-1). The pipe specimens with a circumferential through-wall crack were subjected four point bending load at 300C in air. Japanese STS410 carbon steel pipe material was found to have high toughness under dynamic loading condition through the CT fracture toughness test. As the results of pipe fracture tests, the maximum moment to pipe fracture under dynamic monotonic and cyclic loading condition, could be estimated by plastic collapse criterion and the effect of dynamic monotonic loading and cyclic loading was a little on the maximum moment to pipe fracture of the STS410 carbon steel pipe. The STS410 carbon steel pipe seemed to be less sensitive to dynamic and cyclic loading effects than the A106Gr.B carbon steel pipe evaluated in IPIRG-1 program

  3. Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings.

    Science.gov (United States)

    Werner, Tomás

    2015-07-01

    Many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring. By generalizing max-sum diffusion (one of convergent message passing algorithms for approximate MAP inference in graphical models), we propose an iterative algorithm to upper bound such partition functions over commutative semirings. The iteration of the algorithm is remarkably simple: change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal. In many commutative semirings, repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide. We call this state marginal consistency. During that, an upper bound on the partition function monotonically decreases. This abstract algorithm unifies several existing algorithms, including max-sum diffusion and basic constraint propagation (or local consistency) algorithms in constraint programming. We further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity (order). Finally, we discuss instances of the framework for several semirings, including the distributive lattice and the max-sum and sum-product semirings.

  4. Wavelet-LMS algorithm-based echo cancellers

    Science.gov (United States)

    Seetharaman, Lalith K.; Rao, Sathyanarayana S.

    2002-12-01

    This paper presents Echo Cancellers based on the Wavelet-LMS Algorithm. The performance of the Least Mean Square Algorithm in Wavelet transform domain is observed and its application in Echo cancellation is analyzed. The Widrow-Hoff Least Mean Square Algorithm is most widely used algorithm for Adaptive filters that function as Echo Cancellers. The present day communication signals are widely non-stationary in nature and some errors crop up when Least Mean Square Algorithm is used for the Echo Cancellers handling such signals. The analysis of non-stationary signals often involves a compromise between how well transitions or discontinuities can be located. The multi-scale or multi-resolution of signal analysis, which is the essence of wavelet transform, makes Wavelets popular in non-stationary signal analysis. In this paper, we present a Wavelet-LMS algorithm wherein the wavelet coefficients of a signal are modified adaptively using the Least Mean Square Algorithm and then reconstructed to give an Echo-free signal. The Echo Canceller based on this Algorithm is found to have a better convergence and a comparatively lesser MSE (Mean Square error).

  5. Analysis and Improvement of Fireworks Algorithm

    Directory of Open Access Journals (Sweden)

    Xi-Guang Li

    2017-02-01

    Full Text Available The Fireworks Algorithm is a recently developed swarm intelligence algorithm to simulate the explosion process of fireworks. Based on the analysis of each operator of Fireworks Algorithm (FWA, this paper improves the FWA and proves that the improved algorithm converges to the global optimal solution with probability 1. The proposed algorithm improves the goal of further boosting performance and achieving global optimization where mainly include the following strategies. Firstly using the opposition-based learning initialization population. Secondly a new explosion amplitude mechanism for the optimal firework is proposed. In addition, the adaptive t-distribution mutation for non-optimal individuals and elite opposition-based learning for the optimal individual are used. Finally, a new selection strategy, namely Disruptive Selection, is proposed to reduce the running time of the algorithm compared with FWA. In our simulation, we apply the CEC2013 standard functions and compare the proposed algorithm (IFWA with SPSO2011, FWA, EFWA and dynFWA. The results show that the proposed algorithm has better overall performance on the test functions.

  6. Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.

    Directory of Open Access Journals (Sweden)

    Kaarina Matilainen

    Full Text Available Estimation of variance components by Monte Carlo (MC expectation maximization (EM restricted maximum likelihood (REML is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR, where the information matrix was generated via sampling; MC average information(AI, where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.

  7. Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion

    Directory of Open Access Journals (Sweden)

    Qiuyu Wang

    2016-06-01

    Full Text Available In this paper, we  propose a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point. This algorithm preserves the computational simplicity of classical proximal gradient algorithm where a singular value decomposition in proximal operator is involved. Global convergence is followed directly in the literature. Numerical results are reported to show the efficiency of the algorithm.

  8. Multidimensional splines for modeling FET nonlinearities

    Energy Technology Data Exchange (ETDEWEB)

    Barby, J A

    1986-01-01

    Circuit simulators like SPICE and timing simulators like MOTIS are used extensively for critical path verification of integrated circuits. MOSFET model evaluation dominates the run time of these simulators. Changes in technology results in costly updates, since modifications require reprogramming of the functions and their derivatives. The computational cost of MOSFET models can be reduced by using multidimensional polynomial splines. Since simulators based on the Newton Raphson algorithm require the function and first derivative, quadratic splines are sufficient for this purpose. The cost of updating the MOSFET model due to technology changes is greatly reduced since splines are derived from a set of points. Crucial for convergence speed of simulators is the fact that MOSFET characteristic equations are monotonic. This must be maintained by any simulation model. The splines the author designed do maintain monotonicity.

  9. Application of hybrid artificial fish swarm algorithm based on similar fragments in VRP

    Science.gov (United States)

    Che, Jinnuo; Zhou, Kang; Zhang, Xueyu; Tong, Xin; Hou, Lingyun; Jia, Shiyu; Zhen, Yiting

    2018-03-01

    Focused on the issue that the decrease of convergence speed and the precision of calculation at the end of the process in Artificial Fish Swarm Algorithm(AFSA) and instability of results, a hybrid AFSA based on similar fragments is proposed. Traditional AFSA enjoys a lot of obvious advantages in solving complex optimization problems like Vehicle Routing Problem(VRP). AFSA have a few limitations such as low convergence speed, low precision and instability of results. In this paper, two improvements are introduced. On the one hand, change the definition of the distance for artificial fish, as well as increase vision field of artificial fish, and the problem of speed and precision can be improved when solving VRP. On the other hand, mix artificial bee colony algorithm(ABC) into AFSA - initialize the population of artificial fish by the ABC, and it solves the problem of instability of results in some extend. The experiment results demonstrate that the optimal solution of the hybrid AFSA is easier to approach the optimal solution of the standard database than the other two algorithms. In conclusion, the hybrid algorithm can effectively solve the problem that instability of results and decrease of convergence speed and the precision of calculation at the end of the process.

  10. Optimization algorithm based on densification and dynamic canonical descent

    Science.gov (United States)

    Bousson, K.; Correia, S. D.

    2006-07-01

    Stochastic methods have gained some popularity in global optimization in that most of them do not assume the cost functions to be differentiable. They have capabilities to avoid being trapped by local optima, and may converge even faster than gradient-based optimization methods on some problems. The present paper proposes an optimization method, which reduces the search space by means of densification curves, coupled with the dynamic canonical descent algorithm. The performances of the new method are shown on several known problems classically used for testing optimization algorithms, and proved to outperform competitive algorithms such as simulated annealing and genetic algorithms.

  11. Log-Linear Model Based Behavior Selection Method for Artificial Fish Swarm Algorithm

    Directory of Open Access Journals (Sweden)

    Zhehuang Huang

    2015-01-01

    Full Text Available Artificial fish swarm algorithm (AFSA is a population based optimization technique inspired by social behavior of fishes. In past several years, AFSA has been successfully applied in many research and application areas. The behavior of fishes has a crucial impact on the performance of AFSA, such as global exploration ability and convergence speed. How to construct and select behaviors of fishes are an important task. To solve these problems, an improved artificial fish swarm algorithm based on log-linear model is proposed and implemented in this paper. There are three main works. Firstly, we proposed a new behavior selection algorithm based on log-linear model which can enhance decision making ability of behavior selection. Secondly, adaptive movement behavior based on adaptive weight is presented, which can dynamically adjust according to the diversity of fishes. Finally, some new behaviors are defined and introduced into artificial fish swarm algorithm at the first time to improve global optimization capability. The experiments on high dimensional function optimization showed that the improved algorithm has more powerful global exploration ability and reasonable convergence speed compared with the standard artificial fish swarm algorithm.

  12. Log-linear model based behavior selection method for artificial fish swarm algorithm.

    Science.gov (United States)

    Huang, Zhehuang; Chen, Yidong

    2015-01-01

    Artificial fish swarm algorithm (AFSA) is a population based optimization technique inspired by social behavior of fishes. In past several years, AFSA has been successfully applied in many research and application areas. The behavior of fishes has a crucial impact on the performance of AFSA, such as global exploration ability and convergence speed. How to construct and select behaviors of fishes are an important task. To solve these problems, an improved artificial fish swarm algorithm based on log-linear model is proposed and implemented in this paper. There are three main works. Firstly, we proposed a new behavior selection algorithm based on log-linear model which can enhance decision making ability of behavior selection. Secondly, adaptive movement behavior based on adaptive weight is presented, which can dynamically adjust according to the diversity of fishes. Finally, some new behaviors are defined and introduced into artificial fish swarm algorithm at the first time to improve global optimization capability. The experiments on high dimensional function optimization showed that the improved algorithm has more powerful global exploration ability and reasonable convergence speed compared with the standard artificial fish swarm algorithm.

  13. Multichannel Filtered-X Error Coded Affine Projection-Like Algorithm with Evolving Order

    Directory of Open Access Journals (Sweden)

    J. G. Avalos

    2017-01-01

    Full Text Available Affine projection (AP algorithms are commonly used to implement active noise control (ANC systems because they provide fast convergence. However, their high computational complexity can restrict their use in certain practical applications. The Error Coded Affine Projection-Like (ECAP-L algorithm has been proposed to reduce the computational burden while maintaining the speed of AP, but no version of this algorithm has been derived for active noise control, for which the adaptive structures are very different from those of other configurations. In this paper, we introduce a version of the ECAP-L for single-channel and multichannel ANC systems. The proposed algorithm is implemented using the conventional filtered-x scheme, which incurs a lower computational cost than the modified filtered-x structure, especially for multichannel systems. Furthermore, we present an evolutionary method that dynamically decreases the projection order in order to reduce the dimensions of the matrix used in the algorithm’s computations. Experimental results demonstrate that the proposed algorithm yields a convergence speed and a final residual error similar to those of AP algorithms. Moreover, it achieves meaningful computational savings, leading to simpler hardware implementation of real-time ANC applications.

  14. Dynamic Inertia Weight Binary Bat Algorithm with Neighborhood Search

    Directory of Open Access Journals (Sweden)

    Xingwang Huang

    2017-01-01

    Full Text Available Binary bat algorithm (BBA is a binary version of the bat algorithm (BA. It has been proven that BBA is competitive compared to other binary heuristic algorithms. Since the update processes of velocity in the algorithm are consistent with BA, in some cases, this algorithm also faces the premature convergence problem. This paper proposes an improved binary bat algorithm (IBBA to solve this problem. To evaluate the performance of IBBA, standard benchmark functions and zero-one knapsack problems have been employed. The numeric results obtained by benchmark functions experiment prove that the proposed approach greatly outperforms the original BBA and binary particle swarm optimization (BPSO. Compared with several other heuristic algorithms on zero-one knapsack problems, it also verifies that the proposed algorithm is more able to avoid local minima.

  15. Evolving Resilient Back-Propagation Algorithm for Energy Efficiency Problem

    Directory of Open Access Journals (Sweden)

    Yang Fei

    2016-01-01

    Full Text Available Energy efficiency is one of our most economical sources of new energy. When it comes to efficient building design, the computation of the heating load (HL and cooling load (CL is required to determine the specifications of the heating and cooling equipment. The objective of this paper is to model heating load and cooling load buildings using neural networks in order to predict HL load and CL load. Rprop with genetic algorithm was proposed to increase the global convergence capability of Rprop by modifying a corresponding weight. Comparison results show that Rprop with GA can successfully improve the global convergence capability of Rprop and achieve lower MSE than other perceptron training algorithms, such as Back-Propagation or original Rprop. In addition, the trained network has better generalization ability and stabilization performance.

  16. Multipartite entangled quantum states: Transformation, Entanglement monotones and Application

    Science.gov (United States)

    Cui, Wei

    Entanglement is one of the fundamental features of quantum information science. Though bipartite entanglement has been analyzed thoroughly in theory and shown to be an important resource in quantum computation and communication protocols, the theory of entanglement shared between more than two parties, which is called multipartite entanglement, is still not complete. Specifically, the classification of multipartite entanglement and the transformation property between different multipartite states by local operators and classical communications (LOCC) are two fundamental questions in the theory of multipartite entanglement. In this thesis, we present results related to the LOCC transformation between multipartite entangled states. Firstly, we investigate the bounds on the LOCC transformation probability between multipartite states, especially the GHZ class states. By analyzing the involvement of 3-tangle and other entanglement measures under weak two-outcome measurement, we derive explicit upper and lower bound on the transformation probability between GHZ class states. After that, we also analyze the transformation between N-party W type states, which is a special class of multipartite entangled states that has an explicit unique expression and a set of analytical entanglement monotones. We present a necessary and sufficient condition for a known upper bound of transformation probability between two N-party W type states to be achieved. We also further investigate a novel entanglement transformation protocol, the random distillation, which transforms multipartite entanglement into bipartite entanglement ii shared by a non-deterministic pair of parties. We find upper bounds for the random distillation protocol for general N-party W type states and find the condition for the upper bounds to be achieved. What is surprising is that the upper bounds correspond to entanglement monotones that can be increased by Separable Operators (SEP), which gives the first set of

  17. Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm

    Czech Academy of Sciences Publication Activity Database

    Foralewski, P.; Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav

    2013-01-01

    Roč. 53, č. 2 (2013), s. 421-432 ISSN 0373-8299 R&D Projects: GA ČR GAP201/10/1920 Institutional support: RVO:67985840 Keywords : Orlicz space * Köthe space * characteristic of monotonicity Subject RIV: BA - General Mathematics

  18. First results of genetic algorithm application in ML image reconstruction in emission tomography

    International Nuclear Information System (INIS)

    Smolik, W.

    1999-01-01

    This paper concerns application of genetic algorithm in maximum likelihood image reconstruction in emission tomography. The example of genetic algorithm for image reconstruction is presented. The genetic algorithm was based on the typical genetic scheme modified due to the nature of solved problem. The convergence of algorithm was examined. The different adaption functions, selection and crossover methods were verified. The algorithm was tested on simulated SPECT data. The obtained results of image reconstruction are discussed. (author)

  19. Modified Backtracking Search Optimization Algorithm Inspired by Simulated Annealing for Constrained Engineering Optimization Problems

    Directory of Open Access Journals (Sweden)

    Hailong Wang

    2018-01-01

    Full Text Available The backtracking search optimization algorithm (BSA is a population-based evolutionary algorithm for numerical optimization problems. BSA has a powerful global exploration capacity while its local exploitation capability is relatively poor. This affects the convergence speed of the algorithm. In this paper, we propose a modified BSA inspired by simulated annealing (BSAISA to overcome the deficiency of BSA. In the BSAISA, the amplitude control factor (F is modified based on the Metropolis criterion in simulated annealing. The redesigned F could be adaptively decreased as the number of iterations increases and it does not introduce extra parameters. A self-adaptive ε-constrained method is used to handle the strict constraints. We compared the performance of the proposed BSAISA with BSA and other well-known algorithms when solving thirteen constrained benchmarks and five engineering design problems. The simulation results demonstrated that BSAISA is more effective than BSA and more competitive with other well-known algorithms in terms of convergence speed.

  20. Distributed k-Means Algorithm and Fuzzy c-Means Algorithm for Sensor Networks Based on Multiagent Consensus Theory.

    Science.gov (United States)

    Qin, Jiahu; Fu, Weiming; Gao, Huijun; Zheng, Wei Xing

    2016-03-03

    This paper is concerned with developing a distributed k-means algorithm and a distributed fuzzy c-means algorithm for wireless sensor networks (WSNs) where each node is equipped with sensors. The underlying topology of the WSN is supposed to be strongly connected. The consensus algorithm in multiagent consensus theory is utilized to exchange the measurement information of the sensors in WSN. To obtain a faster convergence speed as well as a higher possibility of having the global optimum, a distributed k-means++ algorithm is first proposed to find the initial centroids before executing the distributed k-means algorithm and the distributed fuzzy c-means algorithm. The proposed distributed k-means algorithm is capable of partitioning the data observed by the nodes into measure-dependent groups which have small in-group and large out-group distances, while the proposed distributed fuzzy c-means algorithm is capable of partitioning the data observed by the nodes into different measure-dependent groups with degrees of membership values ranging from 0 to 1. Simulation results show that the proposed distributed algorithms can achieve almost the same results as that given by the centralized clustering algorithms.