Time-optimal monotonic convergent algorithms for the control of quantum systems
Lapert, M; Sugny, D
2012-01-01
We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the field fluence. A standard algorithm designs a control field of fixed duration which both brings the system close to the target state and minimizes its fluence, whereas here we include in addition the optimization of the duration in the cost functional. We apply this new algorithm to the control of spin systems in Nuclear Magnetic Resonance. We show how to implement CNOT gates in systems of two and four coupled spins.
A smoothing monotonic convergent optimal control algorithm for NMR pulse sequence design
Maximov, Ivan I; Salomon, Julien; Turinici, Gabriel
2010-01-01
The past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear magnetic resonance (NMR) where natural separation between coherent and dissipative spin dynamics processes has enabled coherent quantum control over long periods of time to shape the experiment to almost ideal adoption to the spin system and external manipulations. This has led to new design principles as well as powerful new experimental methods within magnetic resonance imaging, liquid-state and solid-state NMR spectroscopy. For this development to continue and expand, it is crucially important to constantly improve the underlying numerical algorithms to provide numerical solutions which are optimally compatible with implementation on current instrumentation and at same time are numerically stable and offer fast monotonic convergence towards the target. Addressing such aims, we ...
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.
A POTENTIAL REDUCTION ALGORITHM FOR MONOTONE VARIATIONAL INEQUALITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A potential reduction algorithm is proposed for the solution of monotone variational inequality problems. At each step of the algorithm, a system of linear equations is solved to get the search direction and the Armijo's rule is used to determine the stepsize.It is proved that the algorithm is globally convergent. Computational results are reported.
Strong convergence theorems for maximal monotone mappings in Banach spaces
Zegeye, Habtu
2008-07-01
Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E*. Let be a Lipschitz continuous monotone mapping with A-1(0)[not equal to][empty set]. For given u,x1[set membership, variant]E, let {xn} be generated by the algorithm xn+1:=[beta]nu+(1-[beta]n)(xn-[alpha]nAJxn), n[greater-or-equal, slanted]1, where J is the normalized duality mapping from E into E* and {[lambda]n} and {[theta]n} are real sequences in (0,1) satisfying certain conditions. Then it is proved that, under some mild conditions, {xn} converges strongly to x*[set membership, variant]E where Jx*[set membership, variant]A-1(0). Finally, we apply our convergence theorems to the convex minimization problems.
Convergence of approximations of monotone gradient systems
Zambotti, Lorenzo
2006-01-01
We consider stochastic differential equations in a Hilbert space, perturbed by the gradient of a convex potential. We investigate the problem of convergence of a sequence of such processes. We propose applications of this method to reflecting O.U. processes in infinite dimension, to stochastic partial differential equations with reflection of Cahn-Hilliard type and to interface models.
Block Monotone Iterative Algorithms for Variational Inequalities with Nonlinear Operators
Institute of Scientific and Technical Information of China (English)
Ming-hui Ren; Jin-ping Zeng
2008-01-01
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established.Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
Institute of Scientific and Technical Information of China (English)
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
Convergence for pseudo monotone semiflows on product ordered topological spaces
Yi, Taishan; Huang, Lihong
In this paper, we consider a class of pseudo monotone semiflows, which only enjoy some weak monotonicity properties and are defined on product-ordered topological spaces. Under certain conditions, several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium, which improve and extend some corresponding results already known. Some applications to delay differential equations are presented.
Ultimate generalization to monotonicity for uniform convergence of trigonometric series
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Chaundy and Jolliffe proved that if {a n } is a non-increasing (monotonic) real sequence with lim n →∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∑∞ n=1 a n sin nx is lim n →∞ na n = 0. We generalize (or weaken) the monotonic condition on the coefficient sequence {a n } in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy-Jolliffe theorem in the complex space.
STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES
Institute of Scientific and Technical Information of China (English)
Yongfu SU; Xiaolong QIN
2008-01-01
K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonexpansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial's condition.
Convergence of the natural approximations of piecewise monotone interval maps.
Haydn, Nicolai
2004-06-01
We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which is Lipshitz continuous and for which the densities converge in the bounded variation norm at a logarithmic rate. This shows that in general one cannot expect exponential convergence in the bounded variation norm. Here we prove that if the derivative of the interval map is Holder continuous and its variation is well approximable (gamma-uniform variation for gamma>0), then the densities converge exponentially fast in the norm.
Institute of Scientific and Technical Information of China (English)
袁亚湘
1995-01-01
The DFP method is one of the most famous numerical algorithms for unconstrained optimization. For uniformly convex objective functions convergence properties of the DFP method are studied. Several conditions that can ensure the global convergence of the DFP method are given.
Gollub, Caroline; Kowalewski, Markus; de Vivie-Riedle, Regina
2008-08-15
We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields. A frequency constraint is introduced and derived mathematically correct, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of nonresonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.
A new non-monotone fitness scaling for genetic algorithm
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The properties of selection operators in the genetic algorithm (GA) are studied in detail. It is indicated that the selection of operations is significant for both improving the general fitness of a population and leading to the schema deceptiveness. The stochastic searching characteristics of GA are compared with those of heuristic methods. The influence of selection operators on the GA' s exploration and exploitation is discussed, and the performance of selection operators is evaluated with the premature convergence of the GA taken as an example based on One-Max function. In order to overcome the schema deceptiveness of the GA, a new type of fitness scaling, non monotone scaling, is advanced to enhance the evolutionary ability of a population. The effectiveness of the new scaling method is tested by a trap function and a needle-in-haystack (NiH) function.
A new approximate proximal point algorithm for maximal monotone operator
Institute of Scientific and Technical Information of China (English)
HE; Bingsheng(何炳生); LIAO; Lizhi(廖立志); YANG; Zhenhua(杨振华)
2003-01-01
The problem concerned in this paper is the set-valued equation 0 ∈ T(z) where T is a maximal monotone operator. For given xk and βk ＞ 0, some existing approximate proximal point algorithms take xk+1 = xk such that xk +ek∈ xk + βkT(xk) and||ek|| ≤ηk||xk - xk||, where {ηk} is a non-negative summable sequence. Instead of xk+1 = xk, the new iterate of the proposing method is given by xk+1 = PΩ[xk - ek], where Ω is the domain of T and PΩ(@) denotes the projection on Ω. The convergence is proved under a significantly relaxed restriction supk＞0 ηk ＜ 1.
Energy Technology Data Exchange (ETDEWEB)
Angelis, G I; Kotasidis, F A; Matthews, J C [Imaging, Proteomics and Genomics, MAHSC, University of Manchester, Wolfson Molecular Imaging Centre, Manchester (United Kingdom); Reader, A J [Montreal Neurological Institute, McGill University, Montreal (Canada); Lionheart, W R, E-mail: georgios.angelis@mmic.man.ac.uk [School of Mathematics, University of Manchester, Alan Turing Building, Manchester (United Kingdom)
2011-07-07
Iterative expectation maximization (EM) techniques have been extensively used to solve maximum likelihood (ML) problems in positron emission tomography (PET) image reconstruction. Although EM methods offer a robust approach to solving ML problems, they usually suffer from slow convergence rates. The ordered subsets EM (OSEM) algorithm provides significant improvements in the convergence rate, but it can cycle between estimates converging towards the ML solution of each subset. In contrast, gradient-based methods, such as the recently proposed non-monotonic maximum likelihood (NMML) and the more established preconditioned conjugate gradient (PCG), offer a globally convergent, yet equally fast, alternative to OSEM. Reported results showed that NMML provides faster convergence compared to OSEM; however, it has never been compared to other fast gradient-based methods, like PCG. Therefore, in this work we evaluate the performance of two gradient-based methods (NMML and PCG) and investigate their potential as an alternative to the fast and widely used OSEM. All algorithms were evaluated using 2D simulations, as well as a single [{sup 11}C]DASB clinical brain dataset. Results on simulated 2D data show that both PCG and NMML achieve orders of magnitude faster convergence to the ML solution compared to MLEM and exhibit comparable performance to OSEM. Equally fast performance is observed between OSEM and PCG for clinical 3D data, but NMML seems to perform poorly. However, with the addition of a preconditioner term to the gradient direction, the convergence behaviour of NMML can be substantially improved. Although PCG is a fast convergent algorithm, the use of a (bent) line search increases the complexity of the implementation, as well as the computational time involved per iteration. Contrary to previous reports, NMML offers no clear advantage over OSEM or PCG, for noisy PET data. Therefore, we conclude that there is little evidence to replace OSEM as the algorithm of choice
The global convergence of the non-quasi-Newton methods with non-monotone line search
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved.Numerical experiments showed that the non-monotone line search was more effective.
Directory of Open Access Journals (Sweden)
Plubtieng Somyot
2009-01-01
Full Text Available Abstract We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004, and Iiduka and Takahashi (2008. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
Directory of Open Access Journals (Sweden)
Somyot Plubtieng
2009-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004, and Iiduka and Takahashi (2008. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
On the rate of convergence of the maximum likelihood estimator of a k-monotone density
Institute of Scientific and Technical Information of China (English)
WELLNER; Jon; A
2009-01-01
Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0,A] are obtained under both the Hellinger distance and the Lp(Q) distance,where 1 p < ∞ and Q is a probability measure on [0,A].The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.
On the rate of convergence of the maximum likelihood estimator of a K-monotone density
Institute of Scientific and Technical Information of China (English)
GAO FuChang; WELLNER Jon A
2009-01-01
Bounds for the bracketing entropy of the classes of bounded K-monotone functions on [0, A] are obtained under both the Hellinger distance and the LP(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a K-monotone density.
Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings
Institute of Scientific and Technical Information of China (English)
WEI Li; SU Yong-fu; ZHOU Hai-yun
2008-01-01
In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
Convergence of some leader election algorithms
Directory of Open Access Journals (Sweden)
Svante Janson
2008-08-01
Full Text Available We start with a set of n players. With some probability P(n,k, we kill n-k players; the other ones stay alive, and we repeat with them. What is the distribution of the number X n of phases (or rounds before getting only one player? We present a probabilistic analysis of this algorithm under some conditions on the probability distributions P(n,k, including stochastic monotonicity and the assumption that roughly a fixed proportion α of the players survive in each round. We prove a kind of convergence in distribution for X n - log 1/α n; as in many other similar problems there are oscillations and no true limit distribution, but suitable subsequences converge, and there is an absolutely continuous random variable Z such that d(X n, ⌈Z+ log 1/α n⌉→0, where d is either the total variation distance or the Wasserstein distance. Applications of the general result include the leader election algorithm where players are eliminated by independent coin tosses and a variation of the leader election algorithm proposed by W.R. Franklin 1982. We study the latter algorithm further, including numerical results.
DATA PREORDERING IN GENERALIZED PAV ALGORITHM FOR MONOTONIC REGRESSION
Institute of Scientific and Technical Information of China (English)
Oleg Burdakov; Anders Grimvall; Oleg Sysoev
2006-01-01
Monotonic regression (MR) is a least distance problem with monotonicity constraints induced by a partially ordered data set of observations. In our recent publication [In Ser.Nonconvex Optimization and Its Applications, Springer-Verlag, (2006) 83, pp. 25-33],the Pool-Adjacent-Violators algorithm (PAV) was generalized from completely to partially ordered data sets (posets). The new algorithm, called GPAV, is characterized by the very low computational complexity, which is of second order in the number of observations.It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The GPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted GPAV solution is optimal. Furthermore, we present results of extensive numerical experiments,from which we draw conclusions about the most and the least preferable topological orders.
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.
Directory of Open Access Journals (Sweden)
Kamonrat Nammanee
2012-01-01
Full Text Available We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.
Convergence of some leader election algorithms
Janson, Svante; Louchard, Guy
2008-01-01
We start with a set of n players. With some probability P(n,k), we kill n-k players; the other ones stay alive, and we repeat with them. What is the distribution of the number X_n of phases (or rounds) before getting only one player? We present a probabilistic analysis of this algorithm under some conditions on the probability distributions P(n,k), including stochastic monotonicity and the assumption that roughly a fixed proportion alpha of the players survive in each round. We prove a kind of convergence in distribution for X_n-log_a n, where the basis a=1/alpha; as in many other similar problems there are oscillations and no true limit distribution, but suitable subsequences converge, and there is an absolutely continuous random variable Z such that the distribution of X_n can be approximated by Z+log_a n rounded to the nearest larger integer. Applications of the general result include the leader election algorithm where players are eliminated by independent coin tosses and a variation of the leader electio...
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2016-03-01
In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.
Convergence of BP Algorithm for Training MLP with Linear Output
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The capability of multilayer perceptrons (MLPs) for approximating continuous functions with arbitrary accuracy has been demonstrated in the past decades. Back propagation (BP) algorithm is the most popular learning algorithm for training of MLPs. In this paper, a simple iteration formula is used to select the learning rate for each cycle of training procedure, and a convergence result is presented for the BP algorithm for training MLP with a hidden layer and a linear output unit. The monotonicity of the error function is also guaranteed during the training iteration.
H∞ approach to monotonically convergent ILC for uncertain time-varying delay systems
Meng, Deyuan; Jia, Yingmin; Du, Junping
2015-01-01
This paper deals with iterative learning control (ILC) design for uncertain time-delay systems. Monotonic convergence of the resulting ILC process is studied, and a sufficient condition within an H∞-based framework is developed. It is shown that under this framework, delay-dependent conditions can be obtained in terms of linear matrix inequalities (LMIs), together with formulas for gain matrices design. A numerical example is provided to illustrate the effectiveness of the robust H∞-based approach to ILC designed via LMIs.
Cominetti, R.; Peypouquet, J.; Sorin, S.
We consider the Tikhonov-like dynamics -u˙(t)∈A(u(t))+ɛ(t)u(t) where A is a maximal monotone operator on a Hilbert space and the parameter function ɛ(t) tends to 0 as t→∞ with ∫0∞ɛ(t) dt=∞. When A is the subdifferential of a closed proper convex function f, we establish strong convergence of u(t) towards the least-norm minimizer of f. In the general case we prove strong convergence towards the least-norm point in A(0) provided that the function ɛ(t) has bounded variation, and provide a counterexample when this property fails.
Comparison of two approximal proximal point algorithms for monotone variational inequalities
Institute of Scientific and Technical Information of China (English)
TAO Min
2007-01-01
Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA (APPA)are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ.For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration.And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm Ⅱ is feasible and easy to implement with relatively low computation load.
Convergence Time Evaluation of Algorithms in MANETs
Patil, Annapurna P; Chunhaviriyakul, Krittaya
2009-01-01
Since the advent of wireless communication, the need for mobile ad hoc networks has been growing exponentially. This has opened up a Pandoras Box of algorithms for dealing with mobile ad hoc networks, or MANETs, as they are generally referred to. Most attempts made at evaluating these algorithms so far have focused on parameters such as throughput, packet delivery ratio, overhead etc. An analysis of the convergence times of these algorithms is still an open issue. The work carried out fills this gap by evaluating the algorithms on the basis of convergence time. Algorithms for MANETs can be classified into three categories: reactive, proactive, and hybrid protocols. In this project, we compare the convergence times of representative algorithms in each category, namely Ad hoc On Demand Distance Vector (AODV) reactive, Destination Sequence Distance Vector protocol (DSDV) proactive, and Temporally Ordered Routing Algorithm (TORA) hybrid. The algorithm performances are compared by simulating them in ns2. Tcl is us...
How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms
Németh, A B
2012-01-01
The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too.
Institute of Scientific and Technical Information of China (English)
LI Hong-gang; PAN Xian-bing
2008-01-01
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian [Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108].
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions.
Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem
Byrne, Charles; Gibali, Aviv; Reich, Simeon
2011-01-01
We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two set-valued mappings entails finding a zero of a maximal monotone mapping in one space, the image of which under a given bounded linear transformation is a zero of another maximal monotone mapping. We present three iterative algorithms that solve such problems in Hilbert space, and establish weak convergence for one and strong convergence for the other two.
Convergent algorithms for protein structural alignment
Directory of Open Access Journals (Sweden)
Martínez José
2007-08-01
Full Text Available Abstract Background Many algorithms exist for protein structural alignment, based on internal protein coordinates or on explicit superposition of the structures. These methods are usually successful for detecting structural similarities. However, current practical methods are seldom supported by convergence theories. In particular, although the goal of each algorithm is to maximize some scoring function, there is no practical method that theoretically guarantees score maximization. A practical algorithm with solid convergence properties would be useful for the refinement of protein folding maps, and for the development of new scores designed to be correlated with functional similarity. Results In this work, the maximization of scoring functions in protein alignment is interpreted as a Low Order Value Optimization (LOVO problem. The new interpretation provides a framework for the development of algorithms based on well established methods of continuous optimization. The resulting algorithms are convergent and increase the scoring functions at every iteration. The solutions obtained are critical points of the scoring functions. Two algorithms are introduced: One is based on the maximization of the scoring function with Dynamic Programming followed by the continuous maximization of the same score, with respect to the protein position, using a smooth Newtonian method. The second algorithm replaces the Dynamic Programming step by a fast procedure for computing the correspondence between Cα atoms. The algorithms are shown to be very effective for the maximization of the STRUCTAL score. Conclusion The interpretation of protein alignment as a LOVO problem provides a new theoretical framework for the development of convergent protein alignment algorithms. These algorithms are shown to be very reliable for the maximization of the STRUCTAL score, and other distance-dependent scores may be optimized with same strategy. The improved score optimization
DEFF Research Database (Denmark)
Garde, Henrik; Staboulis, Stratos
2016-01-01
demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity......The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property...... of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We...
Institute of Scientific and Technical Information of China (English)
Sun Qingying
2005-01-01
In this paper, a new class of three term memory gradient method with nonmonotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
Institute of Scientific and Technical Information of China (English)
LIU Yong; BAI Yan-qin
2009-01-01
A polynomial interior-point algorithm is presented for monotone linear complementarity problem (MLCP) based on:a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.
Polyclonal clustering algorithm and its convergence
Institute of Scientific and Technical Information of China (English)
MA Li; JIAO Li-cheng; BAI Lin; CHEN Chang-guo
2008-01-01
Being characteristic of non-teacher learning, self-organization, memory, and noise resistance, the artificial immune system is a research focus in the field of intelligent information processing. Based on the basic principles of organism immune and clonal selection, this article presents a polyclonal clustering algorithm characteristic of self-adaptation. According to the core idea of the algorithm, various immune operators in the artificial immune system are employed in the clustering process; moreover, clustering numbers are adjusted in accordance with the affinity function. Introduction of the recombination operator can effectively enhance the diversity of the individual antibody in a generation population, so that the searching scope for solutions is enlarged and the premature phenomenon of the algorithm is avoided. Besides, introduction of the inconsistent mutation operator enhances the adaptability and optimizes the performance of local solution seeking. Meanwhile, the convergence of the algorithm is accelerated. In addition, the article also proves the convergence of the algorithm by employing the Markov chain. Results of the data simulation experiment show that the algorithm is capable of obtaining reasonable and effective cluster.
Directory of Open Access Journals (Sweden)
Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
Limit points of the monotonic schemes
Salomon, J
2005-01-01
Many numerical simulations in quantum (bilinear) control use the monotonically convergent algorithms of Krotov (introduced by Tannor), Zhu & Rabitz or the general form of Maday & Turinici. This paper presents an analysis of the limit set of controls provided by these algorithms and a proof of convergence in a particular case.
Convergence Rates of Finite Difference Stochastic Approximation Algorithms
2016-06-01
examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm , under various updating schemes using finite...dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...Kiefer-Wolfowitz algorithm , mirror descent algorithm , finite-difference approximation, Monte Carlo methods REPORT DOCUMENTATION PAGE 11. SPONSOR
A predictor-corrector interior-point algorithm for monotone variational inequality problems
Institute of Scientific and Technical Information of China (English)
梁昔明; 钱积新
2002-01-01
Mehrotra's recent suggestion of a predictor-corrector variant of primal-dual interior-point method for linear programming is currently the interior-point method of choice for linear programming. In this work the authors give a predictor-corrector interior-point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.
Exponentially Convergent Algorithms for Abstract Differential Equations
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
A weakly monotonic backward induction algorithm on finite bounded subsets of vector lattices
Dragut, A. B.
2004-03-01
We present a new efficient and robust backward induction algorithm, which is weakly monotonic, working on bounded subsets without holes of lattices. We prove all its properties, give examples of applications, and illustrate its behavior, comparing it with the natural extension of the unidimensional algorithm presented in Puterman (Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley, New York, 1994), in the sense of Topkis (Frontiers of Economic Research Series, Princeton University Press, Princeton, NJ, 1998) and White (Recent Developments in Markov Decision Processes, Academic Press, New York, 1980, 261) and showing, also experimentally, that it is much more efficient.
Directory of Open Access Journals (Sweden)
Cho SunYoung
2010-01-01
Full Text Available Abstract The purpose of this paper is to consider the weak convergence of an iterative sequence for finding a common element in the set of solutions of generalized equilibrium problems, in the set of solutions of classical variational inequalities, and in the set of fixed points of nonexpansive mappings.
DasGupta, Bhaskar; Enciso, German Andres; Sontag, Eduardo; Zhang, Yi
2007-01-01
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson [Goemans, M., Williamson, D., 1995. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42 (6), 1115-1145]. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.
Convergence Time and Phase Transition in a Non-monotonic Family of Probabilistic Cellular Automata
Ramos, A. D.; Leite, A.
2017-08-01
In dynamical systems, some of the most important questions are related to phase transitions and convergence time. We consider a one-dimensional probabilistic cellular automaton where their components assume two possible states, zero and one, and interact with their two nearest neighbors at each time step. Under the local interaction, if the component is in the same state as its two neighbors, it does not change its state. In the other cases, a component in state zero turns into a one with probability α , and a component in state one turns into a zero with probability 1-β . For certain values of α and β , we show that the process will always converge weakly to δ 0, the measure concentrated on the configuration where all the components are zeros. Moreover, the mean time of this convergence is finite, and we describe an upper bound in this case, which is a linear function of the initial distribution. We also demonstrate an application of our results to the percolation PCA. Finally, we use mean-field approximation and Monte Carlo simulations to show coexistence of three distinct behaviours for some values of parameters α and β.
Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm
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.
Maximum-entropy clustering algorithm and its global convergence analysis
Institute of Scientific and Technical Information of China (English)
无
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.
改进Gauss-Seide方法的收敛速度的单调性%On the Monotonicity of Convergence Rate of Modified Gauss-Seidel Method
Institute of Scientific and Technical Information of China (English)
庄伟芬; 卢琳璋
2004-01-01
In this note, we prove that the convergence rate of the modified Gauss-Seidel (MGS) method with preconditional I + Sα is a monotonic function of preconditioning parameter a. Based on this result, to achieve better convergence rate we suggest proforming twice preconditoning when applying the MGS method to solve a linear system whose coefficient matrix is an irreducible non-singular M-matrix.
一类基于单调映射的松弛投影算法%A Relaxed Proximal Point Algorithm Based on Monotonicity Mapping
Institute of Scientific and Technical Information of China (English)
李观荣
2011-01-01
A relaxed proximal point algorithm based on the notion of A-maximal（m）-relaxed Monotonicity is developed,and then the convergence analysis in the context of solving a general class of variational inclusions is examined.The results in this context improve some known results in the literature.%构造了一类基于A-极大（m）-松弛单调映射的松弛投影算法,并给出了基于变分包含问题的收敛分析.文章的结论推广了相关文献的结论.
Convergence of algorithms used for principal component analysis
Institute of Scientific and Technical Information of China (English)
张俊华; 陈翰馥
1997-01-01
The convergence of algorithms used for principal component analysis is analyzed. The algorithms are proved to converge to eigenvectors and eigenvalues of a matrix A which is the expectation of observed random samples. The conditions required here are considerably weaker than those used in previous work.
CONVERGENCE RATE OF A GENERALIZED ADDITIVE SCHWARZ ALGORITHM
Institute of Scientific and Technical Information of China (English)
Jin-ping Zeng; Gao-jie Chen
2006-01-01
The convergence rate of a generalized additive Schwarz algorithm for solving boundary value problems of elliptic partial differential equations is studied. A quantitative analysis of the convergence rate is given for the model Dirichlet problem. It will be shown that a greater acceleration of the algorithm can be obtained by choosing the parameter suitably.Some numerical tests are also presented in this paper.
The analysis of the convergence of ant colony optimization algorithm
Institute of Scientific and Technical Information of China (English)
ZHU Qingbao; WANG Lingling
2007-01-01
The ant colony optimization algorithm has been widely studied and many important results have been obtained.Though this algorithm has been applied to many fields.the analysis about its convergence is much less,which will influence the improvement of this algorithm.Therefore,the convergence of this algorithm applied to the traveling salesman problem(TSP)was analyzed in detail.The conclusion that this algorithm will definitely converge to the optimal solution under the condition of 0＜q0＜1 was proved true.In addition,the influence on its convergence caused by the properties of the closed path,heuristic functions,the pheromone and q0 was analyzed.Based on the above-mentioned,some conclusions about how to improve the speed of its convergence are obtained.
SUPERLINEAR CONVERGENCE OF THE DFP ALGORITHM WITHOUT EXACT LINE SEARCH
Institute of Scientific and Technical Information of China (English)
濮定国
2001-01-01
@@ Broyden algorithms are very efficient methods for solving the nonlinear programming problem: min {f(x); x ∈ Rn}. (1) With exact line search, Powell[1] proved that the rate of convergence of these algorithms is one-step Q-superlinear for a twice continuously differentiable and uniformly convex function,and pu[2] extended this result for LC1 function. Pu and Yu[3] proved that if the points which are given by these algorithms are convergent they are globally convergent for continuously differentiable functions without convexity.
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
A Convergent Iterative Algorithm for Solving Elastic Waveform Inversion
Institute of Scientific and Technical Information of China (English)
张剑锋
1994-01-01
The numerical method for elastic waveform inversion is studied and a convergent iterative algorithm is achieved by designing vinual source and altering objective function of the optimization solution in the computational process, which enables the solutions to converge to the real values and improves the convergence rate by changing the property of curved surface of the objective function, thus opening a new way for further developing the optimization solution of inverse problems.
A fast algorithm for nonnegative matrix factorization and its convergence.
Li, Li-Xin; Wu, Lin; Zhang, Hui-Sheng; Wu, Fang-Xiang
2014-10-01
Nonnegative matrix factorization (NMF) has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the NMF. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, the convergence of multiplicative update algorithms has not been well resolved. This paper first discusses the convergence of existing multiplicative update algorithms. We then propose a new multiplicative update algorithm for minimizing the Euclidean distance between approximate and true values. Based on the optimization principle and the auxiliary function method, we prove that our new algorithm not only converges to a stationary point, but also does faster than existing ones. To verify our theoretical results, the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods.
Characteristic analysis and prevention on premature convergence in genetic algorithms
Institute of Scientific and Technical Information of China (English)
徐宗本; 高勇
1997-01-01
The identification and characteristics of premature convergence in genetic algorithms (GAs) are investigated Through a detailed quantitative analysis on the search capability and the degree of population diversity, the cause of premature convergence in GAs is recognized, and attributed to the maturation effect of the GAs: The minimum schema deduced from current population, which is the largest search space of a GA, converges to a homogeneous population in probability 1 ( so the search capability of the GA decreases and premature convergence occurs). It is shown that, as quantitative features of the maturation effect, the degree of population diversity converges to zero with probability 1, and the tendency for premature convergence is inversely proportional to the population size and directly proportional to the variance of the fitness ratio of zero allele at any gene position of the current population. Based on the theoretical analysis, several strategies for preventing premature convergence are suggest
Convergence of Hybrid Space Mapping Algorithms
DEFF Research Database (Denmark)
Madsen, Kaj; Søndergaard, Jacob
2004-01-01
\\$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......The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It may be considered a preprocessing method which often provides a very efficient initial phase of an optimization procedure. However, the ultimate rate of convergence...... 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...
Convergence of Hybrid Space Mapping Algorithms
DEFF Research Database (Denmark)
Madsen, Kaj; Søndergaard, Jacob
2004-01-01
\\$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......The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It may be considered a preprocessing method which often provides a very efficient initial phase of an optimization procedure. However, the ultimate rate of convergence...... 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...
Bayesian Optimization Algorithm, Population Sizing, and Time to Convergence
Energy Technology Data Exchange (ETDEWEB)
Pelikan, M.; Goldberg, D.E.; Cantu-Paz, E.
2000-01-19
This paper analyzes convergence properties of the Bayesian optimization algorithm (BOA). It settles the BOA into the framework of problem decomposition used frequently in order to model and understand the behavior of simple genetic algorithms. The growth of the population size and the number of generations until convergence with respect to the size of a problem is theoretically analyzed. The theoretical results are supported by a number of experiments.
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.
Global annealing genetic algorithm and its convergence analysis
Institute of Scientific and Technical Information of China (English)
张讲社; 徐宗本; 梁怡
1997-01-01
A new selection mechanism termed global annealing selection (GAnS) is proposed for the genetic algorithm. It is proved that the GAnS genetic algorithm converges to the global optimums if and only if the parents are allowed to compete for reproduction, and that the variance of population’s fitness can be used as a natural stopping criterion. Numerical simulations show that the new algorithm has stronger ability to escape from local maximum and converges more rapidly than canonical genetic algorithm.
Counterexamples to convergence theorem of maximum-entropy clustering algorithm
Institute of Scientific and Technical Information of China (English)
于剑; 石洪波; 黄厚宽; 孙喜晨; 程乾生
2003-01-01
In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases.
Institute of Scientific and Technical Information of China (English)
史沧红; 吴定平
2013-01-01
针对Yonghong Yao等给出的在Hilbert空间中单个非扩张映射和单调映射的迭代算法,和目前对非扩张映射族和其他映射之间迭代方法研究较少的前提下,结合Tomco Shimizu等给出的在Hilbert空间中非扩张映射族的迭代算法,提出了非扩张映射族与α-逆-强单调映射的迭代算法.通过建立相应的收敛性定理,利用迭代算法,得到非扩张映射族公共不动点集和α-逆-强单调映射变分不等式解集的公共元.研究结果表明这个迭代序列强收敛于这一公共元.%Based on the terative algorithm of a nonexpansive mapping and a monotone mapping in Hilbert spaces given by Yonghong Yao etc, under the situation that currently less iterative method between nonexpansive mapping families and other mappings are studied, integrating the iterative algorithm for families of nonexpansive mappings in Hilbert spaces given by Tomoo Shimizu etc, we introduce a new iterative scheme of nonexpansive families mappings and α-inverse-strongly monotone mappings. Through the establishment of a strong convergence theorem and by using the new iterative algorithm, we got the common element of the set of fixed points of families of nonexpansive mappings and the set of solutions of the variational for α-inverse-strongly monotone mappings. The results show that the iterative scheme converges strongly to the common element.
Convergence properties of the softassign quadratic assignment algorithm.
Rangarajan, A; Vuille, A; Mjolsness, E
1999-08-15
The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.
Convergence results on iteration algorithms to linear systems.
Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo
2014-01-01
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.
Improving the convergence of an iterative algorithm proposed by Waxman
Berger, W. A.; Miller, H. G.
2006-11-01
In an iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical relationship between the coupling constant of the potential and the ground state eigenvalue is obtained which can be used to make the algorithm more efficient.
Improving the Convergence of an Iterative Algorithm Proposed By Waxman
Berger, W A
2006-01-01
In the iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical relationship between the coupling constant of the potential and the ground state eigenvalue is obtained which can be used to make the algorithm more efficient.
A FAST CONVERGING SPARSE RECONSTRUCTION ALGORITHM IN GHOST IMAGING
Institute of Scientific and Technical Information of China (English)
Li Enrong; Chen Mingliang; Gong Wenlin; Wang Hui; Han Shensheng
2012-01-01
A fast converging sparse reconstruction algorithm in ghost imaging is presented.It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex optimization.Tests using experimental data show that,compared with the algorithm of Gradient Projection for Sparse Reconstruction (GPSR),the proposed algorithm yields better results with less computation work.
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.
On the convergence of inexact Uzawa algorithms
Energy Technology Data Exchange (ETDEWEB)
Welfert, B.D. [Arizona State Univ., Tempe, AZ (United States)
1994-12-31
The author considers the solution of symmetric indefinite systems which can be cast in matrix block form, where diagonal blocks A and C are symmetric positive definite and semi-definite, respectively. Systems of this type arise frequently in quadratic minimization problems, as well as mixed finite element discretizations of fluid flow equation. The author uses the Uzawa algorithm to precondition the matrix equations.
Linearly convergent inexact proximal point algorithm for minimization. Revision 1
Energy Technology Data Exchange (ETDEWEB)
Zhu, C.
1993-08-01
In this paper, we propose a linearly convergent inexact PPA for minimization, where the inner loop stops when the relative reduction on the residue (defined as the objective value minus the optimal value) of the inner loop subproblem meets some preassigned constant. This inner loop stopping criterion can be achieved in a fixed number of iterations if the inner loop algorithm has a linear rate on the regularized subproblems. Therefore the algorithm is able to avoid the computationally expensive process of solving the inner loop subproblems exactly or asymptotically accurately; a process required by most of the other linearly convergent PPAs. As applications of this inexact PPA, we develop linearly convergent iteration schemes for minimizing functions with singular Hessian matrices, and for solving hemiquadratic extended linear-quadratic programming problems. We also prove that Correa-Lemarechal`s ``implementable form`` of PPA converges linearly under mild conditions.
Institute of Scientific and Technical Information of China (English)
童小娇; 周叔子
2000-01-01
A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.
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.
ARTIFICIAL IMMUNE ALGORITHM OF MULTICELLULAR GROUP AND ITS CONVERGENCE
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Objective To find out more extrema simultaneously including global optimum and multiple local optima existed in multi-modal functions. Methods Germinal center is the generator and selector of high-affinity B cells, a multicellular group's artificial immune algorithm was proposed based on the germinal center reaction mechanism of natural immune systems. Main steps of the algorithm were given, including hyper-mutation, selection, memory, similarity suppression and recruitment of B cells and the convergence of it was proved. Results The algorithm has been tested to optimize various multi-modal functions, and the simulation results show that the artificial immune algorithm proposed here can find multiple extremum of these functions with lower computational cost. Conclusion The algorithm is valid and can converge on the satisfactory solution set D with probability 1 and approach to global solution and many local optimal solutions existed.
Frequency domain simultaneous algebraic reconstruction techniques: algorithm and convergence
Wang, Jiong; Zheng, Yibin
2005-03-01
We propose a simultaneous algebraic reconstruction technique (SART) in the frequency domain for linear imaging problems. This algorithm has the advantage of efficiently incorporating pixel correlations in an a priori image model. First it is shown that the generalized SART algorithm converges to the weighted minimum norm solution of a weighted least square problem. Then an implementation in the frequency domain is described. The performance of the new algorithm is demonstrated with fan beam computed tomography (CT) examples. Compared to the traditional SART and its major alternative ART, the new algorithm offers superior image quality and potential application to other modalities.
Convergence and Cycling in Walker-type Saddle Search Algorithms
Levitt, Antoine
2016-01-01
Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present results for idealized versions of the dimer and gentlest ascent (GAD) saddle search algorithms that show-case the limitations of what is theoretically achievable within the current class of saddle search algorithms: (1) we present an improved estimate on the region of attraction of saddles; and (2) we construct quasi-periodic solutions which indicate that it is impossible to obtain globally convergent variants of dimer and GAD type algorithms.
Degree Fluctuations and the Convergence Time of Consensus Algorithms
Olshevsky, Alex
2011-01-01
We consider a consensus algorithm in which every node in a time-varying undirected connected graph assigns equal weight to each of its neighbors. Under the assumption that the degree of any given node is constant in time, we show that the algorithm achieves consensus within a given accuracy epsilon on n nodes in time O(n^3 log(n/epsilon)). Because there is a direct relation between consensus algorithms in time-varying environments and inhomogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give simple proofs that the convergence time becomes exponentially large in the number of nodes n under slight relaxations of the above assumptions. We prove that exponential convergence time is possible for consensus algorithms on fixed directed graphs, and we use an example of Cao, Spielman, and Morse to give a simple argument that the same is possible if the constant degrees assumption is even slightly relaxed.
Stochastic analysis and convergence velocity estimation of genetic algorithms
Institute of Scientific and Technical Information of China (English)
郭观七; 喻寿益
2003-01-01
Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is proved that inadequate parameters of mutation and crossover probabilities degenerate standard genetic algorithm to a class of random search algorithms without selection bias toward any solution based on fitness. After introducing elitist reservation, the stochastic matrix of Markov chain of the best-so-far individual with the highest fitness is derived.The average convergence velocity of genetic algorithms is defined as the mathematical expectation of the mean absorbing time steps that the best-so-far individual transfers from any initial solution to the global optimum. Using the stochastic matrix of the best-so-far individual, a theoretic method and the computing process of estimating the average convergence velocity are proposed.
A Rapidly Convergence Algorithm for Linear Search and its Application
Institute of Scientific and Technical Information of China (English)
Jianliang Li; Hua Zhu; Xianzhong Zhou; Wenjing Song
2006-01-01
The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the adwantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bj(o)rck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems
Institute of Scientific and Technical Information of China (English)
Jin-bao Jian; Ran Quan; Qing-jie Hu
2007-01-01
In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming (SQP), a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming (QP) which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.
Optimization Algorithms Testing and Convergence by Using a Stacked Histogram
Directory of Open Access Journals (Sweden)
ZAPLATILEK, K.
2011-02-01
Full Text Available The article describes an original method of optimization algorithms testing and convergence. The method is based on so-called stacked histogram. Stacked histogram is a histogram with its features marked by a chosen colour scheme. Thus, the histogram maintains the information on the input digital sequence. This approach enables an easy identification of the hidden defects in the random process statistical distribution. The stacked histogram is used for the testing of the convergent quality of various optimization techniques. Its width, position and colour scheme provides enough information on the chosen algorithm optimization trajectory. Both the classic iteration techniques and the stochastic optimization algorithm with the adaptation were used as examples.
Convergence and refinement of the Wang Landau algorithm
Lee, Hwee Kuan; Okabe, Yutaka; Landau, D. P.
2006-07-01
Recently, Wang and Landau proposed a new random walk algorithm that can be very efficiently applied to many problems. Subsequently, there has been numerous studies on the algorithm itself and many proposals for improvements were put forward. However, fundamental questions such as what determines the rate of convergence has not been answered. To understand the mechanism behind the Wang-Landau method, we did an error analysis and found that a steady state is reached where the fluctuations in the accumulated energy histogram saturate at values proportional to [. This value is closely related to the error corrections to the Wang-Landau method. We also study the rate of convergence using different "tuning" parameters in the algorithm.
On the convergence of the Fitness-Complexity algorithm
Pugliese, Emanuele; Zaccaria, Andrea; Pietronero, Luciano
2016-10-01
We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied.
A globally convergent matricial algorithm for multivariate spectral estimation
Ramponi, Federico; Pavon, Michele
2008-01-01
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate spectral estimation, and test its effectiveness through simulation. Simulation shows that, in the case of short observation records, this method may provide a valid alternative to standard multivariable identification techniques such as MATLAB's PEM and MATLAB's N4SID.
Qin, Jing; Garcia, Tanya P; Ma, Yanyuan; Tang, Ming-Xin; Marder, Karen; Wang, Yuanjia
2014-01-01
In certain genetic studies, clinicians and genetic counselors are interested in estimating the cumulative risk of a disease for individuals with and without a rare deleterious mutation. Estimating the cumulative risk is difficult, however, when the estimates are based on family history data. Often, the genetic mutation status in many family members is unknown; instead, only estimated probabilities of a patient having a certain mutation status are available. Also, ages of disease-onset are subject to right censoring. Existing methods to estimate the cumulative risk using such family-based data only provide estimation at individual time points, and are not guaranteed to be monotonic, nor non-negative. In this paper, we develop a novel method that combines Expectation-Maximization and isotonic regression to estimate the cumulative risk across the entire support. Our estimator is monotonic, satisfies self-consistent estimating equations, and has high power in detecting differences between the cumulative risks of different populations. Application of our estimator to a Parkinson's disease (PD) study provides the age-at-onset distribution of PD in PARK2 mutation carriers and non-carriers, and reveals a significant difference between the distribution in compound heterozygous carriers compared to non-carriers, but not between heterozygous carriers and non-carriers.
Algorithm for correcting optimization convergence errors in Eclipse.
Zacarias, Albert S; Mills, Michael D
2009-10-14
IMRT plans generated in Eclipse use a fast algorithm to evaluate dose for optimization and a more accurate algorithm for a final dose calculation, the Analytical Anisotropic Algorithm. The use of a fast optimization algorithm introduces optimization convergence errors into an IMRT plan. Eclipse has a feature where optimization may be performed on top of an existing base plan. This feature allows for the possibility of arriving at a recursive solution to optimization that relies on the accuracy of the final dose calculation algorithm and not the optimizer algorithm. When an IMRT plan is used as a base plan for a second optimization, the second optimization can compensate for heterogeneity and modulator errors in the original base plan. Plans with the same field arrangement as the initial base plan may be added together by adding the initial plan optimal fluence to the dose correcting plan optimal fluence.A simple procedure to correct for optimization errors is presented that may be implemented in the Eclipse treatment planning system, along with an Excel spreadsheet to add optimized fluence maps together.
Introduction to the New Type of Algorithms for Accelerating Convergence of Sequence
Thukral, R.
2005-01-01
A collection of new algorithms for accelerating the convergence of sequence of functions was described. The definitions and connections of these new algorithms with the improved functional epsilon algorithms are given. The effectiveness of these new algorithms was examined, namely the α-algorithms, the β-algorithms, the γ-algorithms, the δ-algorithms and the improved functional epsilon algorithms, for approximating solutions of a given power series. The esti...
A convergent mean shift algorithm to select targets for LAMOST
Institute of Scientific and Technical Information of China (English)
Guang-Wei Li; Gang Zhao
2009-01-01
This paper firstly finds that the Mean Shift Algorithm used by the Observation Control System (OCS) Research Group of the University of Science and Technology of China in Survey Strategy System 2.10 (SSS2.10) to select targets for the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is not convergent in theory. By carefully studying the mathematical formulation of the Mean Shift Algorithm, we find that it tries to find a point where some objective function achieves its maximum value; the Mean Shift Vector can be regarded as the ascension direction for the objective function. If we regard the objective function as the numerical description for the imaging quality of all targets covered by the focal panel, then the Mean Shift Algorithm can find the place where the imaging quality is the best. So, the problem of selecting targets is equal to the problem of finding the place where the imaging quality is the best. In addition, we also give some effective heuristics to improve computational speed and propose an effective method to assign point sources to the respective fibers. As a result, our program runs fast, and it costs only several seconds to generate an observation.
Online Optimal Controller Design using Evolutionary Algorithm with Convergence Properties
Directory of Open Access Journals (Sweden)
Yousef Alipouri
2014-06-01
Full Text Available Many real-world applications require minimization of a cost function. This function is the criterion that figures out optimally. In the control engineering, this criterion is used in the design of optimal controllers. Cost function optimization has difficulties including calculating gradient function and lack of information about the system and the control loop. In this article, for the first time, gradient memetic evolutionary programming is proposed for minimization of non-convex cost functions that have been defined in control engineering. Moreover, stability and convergence of the proposed algorithm are proved. Besides, it is modified to be used in online optimization. To achieve this, the sign of the gradient function is utilized. For calculating the sign of the gradient, there is no need to know the cost-function’s shape. The gradient functions are estimated by the algorithm. The proposed algorithm is used to design a PI controller for nonlinear benchmark system CSTR (Continuous Stirred Tank Reactor by online and off-line approaches.
Peptide Backbone Sampling Convergence with the Adaptive Biasing Force Algorithm
Faller, Christina E.; Reilly, Kyle A.; Hills, Ronald D.; Guvench, Olgun
2013-01-01
Complete Boltzmann sampling of reaction coordinates in biomolecular systems continues to be a challenge for unbiased molecular dynamics simulations. A growing number of methods have been developed for applying biases to biomolecular systems to enhance sampling while enabling recovery of the unbiased (Boltzmann) distribution of states. The Adaptive Biasing Force (ABF) algorithm is one such method, and works by canceling out the average force along the desired reaction coordinate(s) using an estimate of this force progressively accumulated during the simulation. Upon completion of the simulation, the potential of mean force, and therefore Boltzmann distribution of states, is obtained by integrating this average force. In an effort to characterize the expected performance in applications such as protein loop sampling, ABF was applied to the full ranges of the Ramachandran ϕ/ψ backbone dihedral reaction coordinates for dipeptides of the 20 amino acids using all-atom explicit-water molecular dynamics simulations. Approximately half of the dipeptides exhibited robust and rapid convergence of the potential of mean force as a function of ϕ/ψ in triplicate 50-ns simulations, while the remainder exhibited varying degrees of less complete convergence. The greatest difficulties in achieving converged ABF sampling were seen in the branched-sidechain amino acids threonine and valine, as well as the special case of proline. Proline dipeptide sampling was further complicated by trans-to-cis peptide bond isomerization not observed in unbiased control molecular dynamics simulations. Overall, the ABF method was found to be a robust means of sampling the entire ϕ/ψ reaction coordinate for the 20 amino acids, including high free-energy regions typically inaccessible in standard molecular dynamics simulations. PMID:23215032
A pathway EM-algorithm for estimating vaccine efficacy with a non-monotone validation set.
Yang, Yang; Halloran, M Elizabeth; Chen, Yanjun; Kenah, Eben
2014-09-01
Here, we consider time-to-event data where individuals can experience two or more types of events that are not distinguishable from one another without further confirmation, perhaps by laboratory test. The event type of primary interest can occur only once. The other types of events can recur. If the type of a portion of the events is identified, this forms a validation set. However, even if a random sample of events are tested, confirmations can be missing nonmonotonically, creating uncertainty about whether an individual is still at risk for the event of interest. For example, in a study to estimate efficacy of an influenza vaccine, an individual may experience a sequence of symptomatic respiratory illnesses caused by various pathogens over the season. Often only a limited number of these episodes are confirmed in the laboratory to be influenza-related or not. We propose two novel methods to estimate covariate effects in this survival setting, and subsequently vaccine efficacy. The first is a pathway expectation-maximization (EM) algorithm that takes into account all pathways of event types in an individual compatible with that individual's test outcomes. The pathway EM iteratively estimates baseline hazards that are used to weight possible event types. The second method is a non-iterative pathway piecewise validation method that does not estimate the baseline hazards. These methods are compared with a previous simpler method. Simulation studies suggest mean squared error is lower in the efficacy estimates when the baseline hazards are estimated, especially at higher hazard rates. We use the pathway EM-algorithm to reevaluate the efficacy of a trivalent live-attenuated influenza vaccine during the 2003-2004 influenza season in Temple-Belton, Texas, and compare our results with a previously published analysis. © 2014, The International Biometric Society.
Global Convergence of Adaptive Generalized Predictive Controller Based on Least Squares Algorithm
Institute of Scientific and Technical Information of China (English)
张兴会; 陈增强; 袁著祉
2003-01-01
Some papers on stochastic adaptive control schemes have established convergence algorithm using a leastsquares parameters. With the popular application of GPC, global convergence has become a key problem in automatic control theory. However, now global convergence of GPC has not been established for algorithms in computing a least squares iteration. A generalized model of adaptive generalized predictive control is presented. The global convergebce is also given on the basis of estimating the parameters of GPC by least squares algorithm.
Michalek, Jan; Capek, Martin
2013-05-01
Image registration tasks are often formulated in terms of minimization of a functional consisting of a data fidelity term penalizing the mismatch between the reference and the target image, and a term enforcing smoothness of shift between neighboring pairs of pixels (a min-sum problem). Most methods for deformable image registration use some form of interpolation between matching control points. The interpolation makes it impossible to account for isolated discontinuities in the deformation field that may appear, e.g., when a physical slice of a microscopy specimen is ruptured by the cutting tool. For registration of neighboring physical slices of microscopy specimens with discontinuities, Janácek proposed an L¹-distance data fidelity term and a total variation (TV) smoothness term, and used a graph-cut (GC) based iterative steepest descent algorithm for minimization. The L¹-TV functional is nonconvex; hence a steepest descent algorithm is not guaranteed to converge to the global minimum. Schlesinger presented transformation of max-sum problems to minimization of a dual quantity called problem power, which is--contrary to the original max-sum functional--convex. Based on Schlesinger's solution to max-sum problems we developed an algorithm for L¹-TV minimization by iterative multi-label steepest descent minimization of the convex dual problem. For Schlesinger's subgradient algorithm we proposed a novel step control heuristics that considerably enhances both speed and accuracy compared with standard step size strategies for subgradient methods. It is shown experimentally that our subgradient scheme achieves consistently better image registration than GC in terms of lower values both of the composite L¹-TV functional, and of its components, i.e., the L¹ distance of the images and the transformation smoothness TV, and yields visually acceptable results even in cases where the GC based algorithm fails. The new algorithm allows easy parallelization and can thus be
Institute of Scientific and Technical Information of China (English)
张建军; 王德人
2004-01-01
In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical experiments show that the algorithm is successful.
A LINE SEARCH AND TRUST REGION ALGORITHM WITH TRUST REGION RADIUS CONVERGING TO ZERO
Institute of Scientific and Technical Information of China (English)
Jin-yan Fan; Wen-bao Ai; Qun-ying Zhang
2004-01-01
In this paper, we present a new line search and trust region algorithm for unconstrained optimization problem with the trust region radius converging to zero. The new trust region algorithm performs a backtracking line search from the failed. Point instead of resolving the subproblem when the trial step results in an increase in the objective function. We show that the algorithm preserves the convergence properties of the traditional trust region algorithms. Numerical results are also given.
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…
Institute of Scientific and Technical Information of China (English)
魏利; 周海云
2009-01-01
In this paper,two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed.Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functiohal are discussed,which extend some previous work.
Directory of Open Access Journals (Sweden)
Li Liu
2013-06-01
Full Text Available Electromagnetic tomography technology is a new process tomography technology. The aim of this study is to develop a new image reconstruction algorithm suitable to electromagnetic tomography and verify its convergence. The advantages and development of electromagnetic tomography technology and image reconstruction algorithms are introduced briefly. Based on conjugate gradient algorithm, modified conjugate gradient algorithm for Electromagnetic Tomography (EMT is proposed. Convergence of the modified conjugate gradient algorithm is analyzed. In the light of the lab electromagnetic tomography system, modified conjugate gradient algorithm for reconstructing images is verified. By evaluation of image error and the relevance, regularization algorithm, Landweber algorithm, conjugate gradient algorithm and modified conjugate gradient algorithm are compared. It can draw the conclusion that for different flow patterns, modified conjugate gradient algorithm is superior to other algorithms in the 8 coils electromagnetic tomography lab system.
An adaptive genetic algorithm with diversity-guided mutation and its global convergence property
Institute of Scientific and Technical Information of China (English)
李枚毅; 蔡自兴; 孙国荣
2004-01-01
An adaptive genetic algorithm with diversity-guided mutation, which combines adaptive probabilities of crossover and mutation was proposed. By means of homogeneous finite Markov chains, it is proved that adaptive genetic algorithm with diversity-guided mutation and genetic algorithm with diversity-guided mutation converge to the global optimum if they maintain the best solutions, and the convergence of adaptive genetic algorithms with adaptive probabilities of crossover and mutation was studied. The performances of the above algorithms in optimizing several unimodal and multimodal functions were compared. The results show that for multimodal functions the average convergence generation of the adaptive genetic algorithm with diversity-guided mutation is about 900 less than that of adaptive genetic algorithm with adaptive probabilities and genetic algorithm with diversity-guided mutation, and the adaptive genetic algorithm with diversity-guided mutation does not lead to premature convergence. It is also shown that the better balance between overcoming premature convergence and quickening convergence speed can be gotten.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Based on a differentiable merit function proposed by Taji,et al in "Mathematical Programming,1993,58: 369-383",a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented.Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
两种非单调信赖域算法的数值比较研究%A Numerical Comparison between Two Classes of Non-monotone Trust Region Algorithms
Institute of Scientific and Technical Information of China (English)
陈俊; 张纯
2011-01-01
This paper is aimed at the comparison between two typical non-monotone trust region algorithms for unconstrained optimization. In theory, they both have good convergence properties. The numerical efficiency of the two non-monotone algorithms is the focus of the comparison. Extensive numerical experiments were conducted, making use of the well-known test problems package by J.J. Mot6 et al. [ ACM Transactions on Mathematical Software, 1981,7（ 1 ） ： 17-41 ]. Then the two algorithms were compared by the performance profiles based on the data obtained from the numerical experiments. The analysis indicates that the numerical efficiency of the algorithm NATR is superior to that of the traditional non-monotone trust region algorithm to a certain extent.%目前求解无约束最优化问题的非单调信赖域算法根据其采用的参考函数值的不同主要有两种：一种是传统的基于最大函数值型，一种是基于函数值加权平均型．理论上该两种算法均具有较好的收敛性质，但关于这两种非单调信赖域算法在实际数值计算效率方面的比较还不充分．为此作者利用国际上广泛采用的无约束优化测试函数包（J．J．More et al．ACM Transactions on Mathematical Software，1981，7（1）：17—41）对这两种方法进行大量的数值试验，并采用剖面分析方法对试验数据进行较全面的分析比较，结果表明基于函数值平均权重的非单调信赖域算法其数值效率在一定程度上优于传统的非单调信赖域算法．
Locally converging algorithms for determining the critical temperature in Ising systems
Faraggi, Eshel; Robb, Daniel T.
2008-10-01
We introduce a class of algorithms that converge to criticality automatically, in a way similar to the invaded cluster algorithm. Unlike the invaded cluster algorithm which uses global percolation as a test for criticality, these local algorithms use an average over local observables, specifically the number of satisfied bonds, in a feedback loop which drives the system toward criticality. Two specific algorithms are introduced, the average algorithm and the locally converging Wolff algorithm. We apply these algorithms to study the Ising square lattice and the Ising Bethe lattice. We find reasonable convergence to the critical temperature for both systems under the locally converging Wolff algorithm. We also re-examine the phase diagram of the dilute two-dimensional (2D) Ising model and find results supporting our previously reported conclusions regarding the existence of a local regime of magnetization below the percolations threshold. In addition, the presented algorithms are computationally more efficient than the invaded cluster algorithm, requiring less CPU time and memory.
About the relaxed cocoercivity and the convergence of the proximal point algorithm
Directory of Open Access Journals (Sweden)
Abdellatif Moudafi
2013-10-01
Full Text Available The aim of this paper is to study the convergence of two proximal algorithms via the notion of (α,r-relaxed cocoercivity without Lipschitzian continuity. We will show that this notion is enough to obtain some interesting convergence theorems without any Lipschitz-continuity assumption. The relaxed cocoercivity case is also investigated.
Convergence analysis of filtered-X LMS algorithm with secondary path modeling error
Institute of Scientific and Technical Information of China (English)
SUN Xu; CHEN Duanshi
2003-01-01
A more relaxed sufficient condition for the convergence of filtered-X LMS (FXLMS)algorithm is presented. It is pointed out that if some positive real condition for secondary pathtransfer function and its estimates is satisfied within all the frequency bands, FXLMS algorithmconverges whatever the reference signal is like. But if the above positive real condition is satisfiedonly within some frequency bands, the convergence of FXLMS algorithm is dependent on thedistribution of power spectral density of the reference signal, and the convergence step size isdetermined by the distribution of some specific correlation matrix eigenvalues.Applying the conclusion above to the Delayed LMS (DLMS) algorithm, it is shown thatDLMS algorithm with some error of time delay estimation converges in certain discrete fre-quency bands, and the width of which are determined only by the "time-delay estimation errorfrequency" which is equal to one fourth of the inverse of estimated error of the time delay.
CONVERGENCE RATES FOR A CLASS OF EVOLUTIONARY ALGORITHMS WITH ELITIST STRATEGY
Institute of Scientific and Technical Information of China (English)
丁立新; 康立山
2001-01-01
This paper discusses the convergence rates about a class of evolutionary al-gorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.
A Low Delay and Fast Converging Improved Proportionate Algorithm for Sparse System Identification
Directory of Open Access Journals (Sweden)
Andy W. H. Khong
2007-04-01
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.
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.
Institute of Scientific and Technical Information of China (English)
苏永福; 高俊宇; 周海云
2008-01-01
Matsushita,Takahashi[4]proved a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method(C Q method)in mathematical programming.The purpose of this paper is to modify the hybrid method of Matsushita,Takahashi by monotone CQ method,and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces.The convergence rate of monotone CQ method is faster than the hybrid method of Matsushita,Takahashi.In addition,the Cauchy sequence method is used in this paper without using the Kadec-Klee property.The results of this paper modify and improve the results of Matsushita,Takahashi and some others.
Convergence Analysis of Forgetting Gradient Algorithm by Using Martingale Hyperconvergence Theorem
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The stochastic gradient (SG) algorithm has less of a computational burden than the least squares algorithms, but it can not track time-varying parameters and has a poor convergence rate. In order to improve the tracking properties of the SG algorithm, the forgetting gradient (FG) algorithm is presented, and its convergence is analyzed by using the martingale hyperconvergence theorem. The results show that: (1) for time-invariant deterministic systems, the parameter estimates given by the FG algorithm converge consistently to their true values; (2) for stochastic time-varying systems, the parameter tracking error is bounded, that is, the parameter tracking error is small when both the parameter change rate and the observation noise are small.
Analysis of the diversity of population and convergence of genetic algorithms based on Negentropy
Institute of Scientific and Technical Information of China (English)
Zhang Lianying; Wang Anmin
2005-01-01
With its wide use in different fields, the problem of the convergence of simple genetic algorithms (GAs) has been concerned. In the past, the research on the convergence of GAs was based on Holland' s model theorem. The diversity of the evolutionary population and the convergence of GAs are studied by using the concept of negentropy based on the discussion of the characteristic of GA. Some test functions are used to test the convergence of GAs, and good results have been obtained. It is shown that the global optimization may be obtained by selecting appropriate parameters of simple GAs if the evolution time is enough.
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.
DEFF Research Database (Denmark)
Madsen, Ole Brun; Nielsen, Jens Frederik Dalsgaard; Schiøler, Henrik
2002-01-01
Convergence trends between the WAN Internet area, characterized by best effort service provision, and the real time LAN domain, with requirements for guaranteed services, are identified and discussed. A bilateral evolution is identified, where typical bulk service applications from WAN...
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 ...
System convergence in transport models: algorithms efficiency and output uncertainty
DEFF Research Database (Denmark)
Rich, Jeppe; Nielsen, Otto Anker
2015-01-01
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...... in the MSA process. In connection to DNTM it is shown that MSA works well when applied to travel-time averaging, whereas trip averaging is generally infected by random noise resulting from the assignment model. The latter implies that the minimum uncertainty in the final model output is dictated...
AN IMPLEMENTABLE ALGORITHM AND ITS CONVERGENCE FOR GLOBAL MINIMIZATION WITH CONSTRAINS
Institute of Scientific and Technical Information of China (English)
李善良; 邬冬华; 田蔚文; 张连生
2003-01-01
With the integral-level approach to global optimization, a class of discon-tinuous penalty functions is proposed to solve constrained minimization problems. Inthis paper we propose an implementable algorithm by means of the good point set ofuniform distribution which conquers the default of Monte-Carlo method. At last weprove the convergence of the implementable algorithm.
Convergence acceleration algorithm via an equation related to the lattice Boussinesq equation
He, Yi; Sun, Jian-Qing; Weniger, Ernst Joachim
2011-01-01
The molecule solution of an equation related to the lattice Boussinesq equation is derived with the help of determinantal identities. It is shown that this equation can for certain sequences be used as a numerical convergence acceleration algorithm. Numerical examples with applications of this algorithm are presented.
CONVERGENCE RATE ANALYSIS OF MULTIPLICATIVE SCHWARZ ALGORITHM FOR ELLIPTIC VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
ZENG Jinping; ZHOU Shuzi; WANG Lieheng
2001-01-01
Considering multiplicative Schwarz algorithm for solving algebraic obstacleproblems, we show the geometric convergence of the algorithm by the use of discretemaximun principle. We also get a decay rate bound independent of the meshsize for theiterative error and illustrate the method by some numerical experiments.
Bosch, Carl; Degirmenci, Soysal; Barlow, Jason; Mesika, Assaf; Politte, David G.; O'Sullivan, Joseph A.
2016-05-01
X-ray computed tomography reconstruction for medical, security and industrial applications has evolved through 40 years of experience with rotating gantry scanners using analytic reconstruction techniques such as filtered back projection (FBP). In parallel, research into statistical iterative reconstruction algorithms has evolved to apply to sparse view scanners in nuclear medicine, low data rate scanners in Positron Emission Tomography (PET) [5, 7, 10] and more recently to reduce exposure to ionizing radiation in conventional X-ray CT scanners. Multiple approaches to statistical iterative reconstruction have been developed based primarily on variations of expectation maximization (EM) algorithms. The primary benefit of EM algorithms is the guarantee of convergence that is maintained when iterative corrections are made within the limits of convergent algorithms. The primary disadvantage, however is that strict adherence to correction limits of convergent algorithms extends the number of iterations and ultimate timeline to complete a 3D volumetric reconstruction. Researchers have studied methods to accelerate convergence through more aggressive corrections [1], ordered subsets [1, 3, 4, 9] and spatially variant image updates. In this paper we describe the development of an AM reconstruction algorithm with accelerated convergence for use in a real-time explosive detection application for aviation security. By judiciously applying multiple acceleration techniques and advanced GPU processing architectures, we are able to perform 3D reconstruction of scanned passenger baggage at a rate of 75 slices per second. Analysis of the results on stream of commerce passenger bags demonstrates accelerated convergence by factors of 8 to 15, when comparing images from accelerated and strictly convergent algorithms.
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
Institute of Scientific and Technical Information of China (English)
徐海文
2012-01-01
半正定单调变分不等式CPC算法只需要计算迭代点的函数值,可以解决一类没有显式表达式的半正定单调变分不等式问题.最近A.Nemirovski( SIAM J Optimiz,2005,15:229 - 251.)给出的prox -类算法的计算复杂性分析表明了外梯度算法在满足单调Lipschitz -连续时具有O(1/t)的收敛率；随后相关文献在一定的条件下给出了投影收缩算法、交替方向法和Douglas - Rachford法的计算复杂性分析.受到上述计算复杂性工作的启发,利用半正定单调变分不等式的基本性质和柯西施瓦兹不等式,在一定的假设条件下,给出了半正定单调变分不等式CPC算法O(1/t)收敛率的证明.%The Correction Projection and Contraction Method (CPC Method) can solve a kind of semidefinite monotone variational inequalities without the manifestation expression of function by only computing the function value at the iteration point. Recently, A. Nemirovski (SI AM J Optim,2005,15:229 -251. ) proposed the efficiency estimate of prox-type method, and his analysis indicates that the extragradient method has O( 1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. Subsequently, B. S. He and X. M. Yuan give out the complexity of the projection and contraction method, the alternating direction method as well as the Douglas-Rachford operator splitting method under some appropriate conditions. Inspired by the encouraging achievement in estimating convergence rate, we establish that the CPC method has 0(1/t) convergence rate for semidefinite monotone variational inequality under some suitable conditions by adopting the basic properties of semidefinite monotone variational inequalities and Cauchy Schwarz inequality in this paper.
Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.
He Songnian; Liang Xiao-Lan
2010-01-01
Let be a real Hilbert space and let be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality of finding a point such that , for all , where is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudocontractions. Strong convergence of the algorithms is proved.
Zero-Temperature Limit of a Convergent Algorithm to Minimize the Bethe Free Energy
Werner, Tomas
2011-01-01
After the discovery that fixed points of loopy belief propagation coincide with stationary points of the Bethe free energy, several researchers proposed provably convergent algorithms to directly minimize the Bethe free energy. These algorithms were formulated only for non-zero temperature (thus finding fixed points of the sum-product algorithm) and their possible extension to zero temperature is not obvious. We present the zero-temperature limit of the double-loop algorithm by Heskes, which converges a max-product fixed point. The inner loop of this algorithm is max-sum diffusion. Under certain conditions, the algorithm combines the complementary advantages of the max-product belief propagation and max-sum diffusion (LP relaxation): it yields good approximation of both ground states and max-marginals.
Convergence of iterative image reconstruction algorithms for Digital Breast Tomosynthesis
DEFF Research Database (Denmark)
Sidky, Emil; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
solutions can aid in iterative image reconstruction algorithm design. This issue is particularly acute for iterative image reconstruction in Digital Breast Tomosynthesis (DBT), where the corresponding data model IS particularly poorly conditioned. The impact of this poor conditioning is that iterative......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....... Math. Imag. Vol. 40, pgs 120-145) and apply it to iterative image reconstruction in DBT....
MONOTONIZATION IN GLOBAL OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
WU ZHIYOU; BAI FUSHENG; ZHANG LIANSHENG
2005-01-01
A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existingconvexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.
CONVERGENCE PROPERTIES OF MULTI-DIRECTIONAL PARALLEL ALGORITHMS FOR UNCONSTRAINED MINIMIZATION
Institute of Scientific and Technical Information of China (English)
Cheng-xian Xu; Yue-ting Yang
2005-01-01
Convergence properties of a class of multi-directional parallel quasi-Newton algorithms for the solution of unconstrained minimization problems are studied in this paper. At each iteration these algorithms generate several different quasi-Newton directions, and then apply line searches to determine step lengths along each direction, simultaneously. The next iterate is obtained among these trail points by choosing the lowest point in the sense of function reductions. Different quasi-Newton updating formulas from the Broyden family are used to generate a main sequence of Hessian matrix approximations. Based on the BFGS and the modified BFGS updating formulas, the global and superlinear convergence results are proved. It is observed that all the quasi-Newton directions asymptotically approach the Newton direction in both direction and length when the iterate sequence converges to a local minimum of the objective function, and hence the result of superlinear convergence follows.
DEFF Research Database (Denmark)
Prasad, Ramjee
2009-01-01
This paper presents the main conclusions which can be drawn from the discussions on Future Communication Systems and lessons on Unpredictable Future of Wireless Communication Systems. Future systems beyond the third generation are already under discussions in international bodies, such as ITU, WW...... and R&D programmes worldwide. The incoming era is characterized by the convergence of networks and access technology and the divergence of applications. Future mobile communication systems should bring something more than only faster data or wireless internet access....
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).
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.
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.
Approximating Curve and Strong Convergence of the CQ Algorithm for the Split Feasibility Problem
Directory of Open Access Journals (Sweden)
Xu Hong-Kun
2010-01-01
Full Text Available Using the idea of Tikhonov's regularization, we present properties of the approximating curve for the split feasibility problem (SFP and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, Byrne's CQ algorithm (Byrne, 2002 has only weak convergence. We introduce a modification of Byrne's CQ algorithm in such a way that strong convergence is guaranteed and the limit is also the minimum-norm solution of SFP.
Maximum-entropy clustering algorithm and its global convergence analysis
Institute of Scientific and Technical Information of China (English)
ZHANG; Zhihua
2001-01-01
［1］Bezdek, J. C., Pattern Recognition with Fuzzy Objective Function Algorithm. New York: Plenum, 1981.［2］Krishnapuram, R., Keller, J., A possibilistic approach to clustering, IEEE Trans. on Fuzzy Systems, 1993, 1(2): 98.［3］Yair, E., Zeger, K., Gersho, A., Competitive learning and soft competition for vector quantizer design, IEEE Trans on Signal Processing, 1992, 40(2): 294.［4］Pal, N. R., Bezdek, J. C., Tsao, E. C. K., Generalized clustering networks and Kohonen's self-organizing scheme, IEEE Trans on Neural Networks, 1993, 4(4): 549.［5］Karayiannis, N. B., Bezdek, J. C., Pal, N. R. et al., Repair to GLVQ: a new family of competitive learning schemes, IEEE Trans on Neural Networks, 1996, 7(5): 1062.［6］Karayiannis, N. B., Pai, P. I., Fuzzy algorithms for learning vector quantization, IEEE Trans. on Neural Networks, 1996, 7(5): 1196.［7］Karayiannis, N. B., A methodology for constructing fuzzy algorithms for learning vector quantization, IEEE Trans. on Neural Networks, 1997, 8(3): 505.［8］Karayiannis, N. B., Bezdek, J. C., An integrated approach to fuzzy learning vector quantization and fuzzy C-Means clustering, IEEE Trans. on Fuzzy Systems, 1997, 5(4): 622.［9］Li Xing-si, An efficient approach to nonlinear minimax problems, Chinese Science Bulletin? 1992, 37(10): 802.［10］Li Xing-si, An efficient approach to a class of non-smooth optimization problems, Science in China, Series A,1994, 37(3): 323.［11］. Zangwill, W., Non-linear Programming: A Unified Approach, Englewood Cliffs: Prentice-Hall, 1969.［12］. Fletcher, R., Practical Methods of Optimization,2nd ed., New York: John Wiley & Sons, 1987.［13］. Zhang Zhihua, Zheng Nanning, Wang Tianshu, Behavioral analysis and improving of generalized LVQ neural network, Acta Automatica Sinica, 1999, 25(5): 582.［14］. Kirkpatrick, S., Gelatt, C. D., Vecchi, M. P., Optimization by simulated annealing, Science, 1983, 220(3): 671.［15］. Ross, K., Deterministic annealing for
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 neighbor
Iterative Schemes for Generalized Equilibrium Problem and Two Maximal Monotone Operators
Directory of Open Access Journals (Sweden)
Yao JC
2009-01-01
Full Text Available The purpose of this paper is to introduce and study two new hybrid proximal-point algorithms for finding a common element of the set of solutions to a generalized equilibrium problem and the sets of zeros of two maximal monotone operators in a uniformly smooth and uniformly convex Banach space. We established strong and weak convergence theorems for these two modified hybrid proximal-point algorithms, respectively.
Song, Kai-Sheng
2008-08-01
Many applications in real-time signal, image, and video processing require automatic algorithms for rapid characterizations of signals and images through fast estimation of their underlying statistical distributions. We present fast and globally convergent algorithms for estimating the three-parameter generalized gamma distribution (G Gamma D). The proposed method is based on novel scale-independent shape estimation (SISE) equations. We show that the SISE equations have a unique global root in their semi-infinite domains and the probability that the sample SISE equations have a unique global root tends to one. The consistency of the global root, its scale, and index shape estimators is obtained. Furthermore, we establish that, with probability tending to one, Newton-Raphson (NR) algorithms for solving the sample SISE equations converge globally to the unique root from any initial value in its given domain. In contrast to existing methods, another remarkable novelty is that the sample SISE equations are completely independent of gamma and polygamma functions and involve only elementary mathematical operations, making the algorithms well suited for real-time both hardware and software implementations. The SISE estimators also allow the maximum likelihood (ML) ratio procedure to be carried out for testing the generalized Gaussian distribution (GGD) versus the G Gamma D. Finally, the fast global convergence and accuracy of our algorithms for finite samples are demonstrated by both simulation studies and real image analysis.
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.
Hrstka, O; 10.1016/S0965-9978(03)00113-3
2009-01-01
This paper presents several types of evolutionary algorithms (EAs) used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occurs. First the standard genetic algorithm (SGA) using binary encoding of real values and its unsatisfactory behavior with multimodal problems is briefly reviewed together with some improvements of fighting premature convergence. Two types of real encoded methods based on differential operators are examined in detail: the differential evolution (DE), a very modern and effective method firstly published by R. Storn and K. Price, and the simplified real-coded differential genetic algorithm SADE proposed by the authors. In addition, an improvement of the SADE method, called CERAF technology, enabling the population of solutions to escape from local extremes, is examined. All methods are tested on an identical set of objective functions and a systematic comparison based on a reliable method...
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.
Convergent validity of the ASAM Patient Placement Criteria using a standardized computer algorithm.
Staines, Graham; Kosanke, Nicole; Magura, Stephen; Bali, Priti; Foote, Jeffrey; Deluca, Alexander
2003-01-01
The study examined the convergent validity of the ASAM Patient Placement Criteria (PPC) by comparing Level of Care (LOC) recommendations produced by two alternative methods: a computerdriven algorithm and a "standard" clinical assessment. A cohort of 248 applicants for alcoholism treatment were evaluated at a multi-modality treatment center. The two methods disagreed (58% of cases) more often than they agreed (42%). The algorithm recommended a more intense LOC than the clinician protocol in 81% of the discrepant cases. Four categories of disagreement accounted for 97% of the discrepant cases. Several major sources of disagreement were identified and examined in detail: clinicians' reasoned departures from the PPC rules, conservatism in algorithm LOC recommendations, and measurement overlap between two specific dimensions. In order for the ASAM PPC and its associated algorithm to be embraced by treatment programs, the observed differences in LOC recommendations between the algorithm and "standard" clinical assessment should be resolved.
Directory of Open Access Journals (Sweden)
Fernando A. Auat Cheein
2010-12-01
Full Text Available 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.
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.
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.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC1 CONSTRAINED OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
Ou Yigui; Hou Dingpi
2005-01-01
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subproblem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
Young, William D.
1992-01-01
The application of formal methods to the analysis of computing systems promises to provide higher and higher levels of assurance as the sophistication of our tools and techniques increases. Improvements in tools and techniques come about as we pit the current state of the art against new and challenging problems. A promising area for the application of formal methods is in real-time and distributed computing. Some of the algorithms in this area are both subtle and important. In response to this challenge and as part of an ongoing attempt to verify an implementation of the Interactive Convergence Clock Synchronization Algorithm (ICCSA), we decided to undertake a proof of the correctness of the algorithm using the Boyer-Moore theorem prover. This paper describes our approach to proving the ICCSA using the Boyer-Moore prover.
Beyer, Hans-Georg
2014-01-01
The convergence behaviors of so-called natural evolution strategies (NES) and of the information-geometric optimization (IGO) approach are considered. After a review of the NES/IGO ideas, which are based on information geometry, the implications of this philosophy w.r.t. optimization dynamics are investigated considering the optimization performance on the class of positive quadratic objective functions (the ellipsoid model). Exact differential equations describing the approach to the optimizer are derived and solved. It is rigorously shown that the original NES philosophy optimizing the expected value of the objective functions leads to very slow (i.e., sublinear) convergence toward the optimizer. This is the real reason why state of the art implementations of IGO algorithms optimize the expected value of transformed objective functions, for example, by utility functions based on ranking. It is shown that these utility functions are localized fitness functions that change during the IGO flow. The governing differential equations describing this flow are derived. In the case of convergence, the solutions to these equations exhibit an exponentially fast approach to the optimizer (i.e., linear convergence order). Furthermore, it is proven that the IGO philosophy leads to an adaptation of the covariance matrix that equals in the asymptotic limit-up to a scalar factor-the inverse of the Hessian of the objective function considered.
Institute of Scientific and Technical Information of China (English)
Xie-ping DING; Zhong-bao WANG
2009-01-01
A new system of the set-valued mixed quasi-variational-like inclusions (SS-MQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone opera-tors, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new re-sults have extended and improved previous results.
On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging
Energy Technology Data Exchange (ETDEWEB)
Hicks, M.J.
1996-01-01
Synthetic Aperture Radar (SAR) imaging is a class of coherent range and Doppler signal processing techniques applied to remote sensing. The aperture is synthesized by recording and processing coherent signals at known positions along the flight path. Demands for greater image resolution put an extreme burden on requirements for inertial measurement units that are used to maintain accurate pulse-to-pulse position information. The recently developed Phase Gradient Autofocus algorithm relieves this burden by taking a data-driven digital signal processing approach to estimating the range-invariant phase aberrations due to either uncompensated motions of the SAR platform or to atmospheric turbulence. Although the performance of this four-step algorithm has been demonstrated, its convergence has not been modeled mathematically. A new sensitivity study of algorithm performance is a necessary step towards this model. Insights that are significant to the application of this algorithm to both SAR and to other coherent imaging applications are developed. New details on algorithm implementation identify an easily avoided biased phase estimate. A new algorithm for defining support of the point spread function is proposed, which promises to reduce the number of iterations required even for rural scenes with low signal-to-clutter ratios.
Energy Technology Data Exchange (ETDEWEB)
McNamara, B.
1984-04-01
Tandem and stellarator equilibria at high ..beta.. have proved hard to compute and the relaxation methods of Bauer et al., Chodura and Schluter, Hirshman, Strauss, and Pearlstein et al. have been slow to converge. This paper reports an extension of the low-..beta.. analytic method of Pearlstein, Kaiser, and Newcomb to arbitrary ..beta.. for tandem mirrors which converges in 10 to 20 iterations. Extensions of the method to stellarator equilibria are proposed and are very close to the analytic method of Johnson and Greene - the stellarator expansion. Most of the results of all these calculations can be adequately described by low-..beta.. approximations since the MHD stability limits occur at low ..beta... The tandem mirror, having weak curvature and a long central cell, allows finite Larmor radius effects to eliminate most ballooning modes and offers the possibility of really high average ..beta... This is the interest in developing such three-dimensional numerical algorithms.
Ferrante, Augusto; Ticozzi, Francesco
2009-01-01
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler pseudo-distance, which gives rise to a convex optimization problem. After developing the variational analysis, we discuss the properties of an efficient algorithm for the solution of the corresponding dual problem, based on the iteration of a nonlinear map in a bounded subset of the dual space. Our main result is the proof of local convergence of the latter, established as a consequence of the Central Manifold Theorem. Supported by numerical evidence, we conjecture that, in the mentioned bounded set, the convergence is actually global.
Convergence Rate Evaluation of a DS-CDMA System with Centralized Power Control By Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, we propose an approach to solve the power control issue in a Digital Cellular System(DS-CDMA) cellular system using Genetic Algorithms (GAs). The transmitter power control developed in this paper has been proven to be efficient to control co-channel interference, to increase bandwidth utilization and to balance the comprehensive services that are shared among all the mobiles with attaining a common Signal-to-Interference Ratio (SIR). In this paper, the optimal Centralized Power Control(CPC) vector is characterized and its optimal solution to CPC is presented using GAs, in which First In-First Out (FIFO) stacks and non-linear decreasing functions are derived in the investigation for enforceing the convergence rate. Emphasis is put on the balance of services and convergence rate by using GAs.
Moritz, Gerrit; Hess, Bernd Artur; Reiher, Markus
2005-01-08
The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.
Directory of Open Access Journals (Sweden)
Soodabeh Darzi
Full Text Available An experience oriented-convergence improved gravitational search algorithm (ECGSA based on two new modifications, searching through the best experiments and using of a dynamic gravitational damping coefficient (α, is introduced in this paper. ECGSA saves its best fitness function evaluations and uses those as the agents' positions in searching process. In this way, the optimal found trajectories are retained and the search starts from these trajectories, which allow the algorithm to avoid the local optimums. Also, the agents can move faster in search space to obtain better exploration during the first stage of the searching process and they can converge rapidly to the optimal solution at the final stage of the search process by means of the proposed dynamic gravitational damping coefficient. The performance of ECGSA has been evaluated by applying it to eight standard benchmark functions along with six complicated composite test functions. It is also applied to adaptive beamforming problem as a practical issue to improve the weight vectors computed by minimum variance distortionless response (MVDR beamforming technique. The results of implementation of the proposed algorithm are compared with some well-known heuristic methods and verified the proposed method in both reaching to optimal solutions and robustness.
2012-01-01
We provide two weakly convergent algorithms for finding a zero of the sum of a maximally monotone operator, a cocoercive operator, and the normal cone to a closed vector subspace of a real Hilbert space. The methods exploit the intrinsic structure of the problem by activating explicitly the cocoercive operator in the first step, and taking advantage of a vector space decomposition in the second step. The second step of the first method is a Douglas-Rachford iteration involving the maximally m...
On an Iterative Method for Finding a Zero to the Sum of Two Maximal Monotone Operators
Directory of Open Access Journals (Sweden)
Hongwei Jiao
2014-01-01
Full Text Available In this paper we consider a problem that consists of finding a zero to the sum of two monotone operators. One method for solving such a problem is the forward-backward splitting method. We present some new conditions that guarantee the weak convergence of the forward-backward method. Applications of these results, including variational inequalities and gradient projection algorithms, are also considered.
Directory of Open Access Journals (Sweden)
He Songnian
2010-01-01
Full Text Available Let be a real Hilbert space and let be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality of finding a point such that , for all , where is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudocontractions. Strong convergence of the algorithms is proved.
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.
Energy Technology Data Exchange (ETDEWEB)
Korshunov, A D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2003-10-31
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.
Directory of Open Access Journals (Sweden)
Uamporn Witthayarat
2012-01-01
Full Text Available The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A+M2−1(0 and (B+M1−1(0, where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in this paper extend and improve the corresponding results of Qin et al. 2011 from Hilbert spaces to Banach spaces and Petrot et al. 2011. Moreover, we also apply our results to some applications for solving convex feasibility problems.
Fraanje, P.R.; Verhaegen, M.; Doelman, N.J.
2003-01-01
The Filtered-U LMS algorithm, proposed by Eriksson for active noise control applications, adapts the coefficients of an infinite-impulse response controller. Conditions for global convergence of the Filtered-U LMS algorithm were presented by Wang and Ren (Signal Processing, 73 (1999) 3) and Mosquera
Institute of Scientific and Technical Information of China (English)
DUAN Hai-bin; WANG Dao-bo; YU Xiu-fen
2006-01-01
Although ant colony algorithm for the heuristic solution of hard combinational optimization problems enjoy a rapidly growing popularity, but little is known about its convergence properties. Based on the introduction of the basic principle and mathematical model, a novel approach to the convergence proof that applies directly to the ant colony algorithm is proposed in this paper. Then, a MATLAB GUI- based ant colony algorithm simulation platform is developed, and the interface of this simulation platform is very friendly, easy to use and to modify.
Phien, Ho N; Vidal, Guifré
2014-01-01
We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the time-evolving block decimation (TEBD) algorithm applied to infinite systems in 1D and 2D, where the ground state is encoded, respectively, in a matrix product state (MPS) and in a projected entangled-pair state (PEPS). An important ingredient of the TEBD algorithm (and a main computational bottle-neck, especially with PEPS in 2D) is the computation of the so-called environment, which is used to determine how to optimally truncate the bond indices of the tensor network so that their dimension is kept constant. In current algorithms, the environment is computed at each step of the imaginary time evolution, to account for the changes that the time evolution introduces in the many-body state represented by the tensor network. Our key insight is that close to convergence, most ...
On a Monotone Ill-posed Problem
Institute of Scientific and Technical Information of China (English)
Nguyen BUONG
2005-01-01
A class of a posteriori parameter choice strategies for the operator version of Tikhonovregularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill-posed nonlinear equation involving a monotone operator in Banach space.
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.
Institute of Scientific and Technical Information of China (English)
Hong Xia YIN; Dong Lei DU
2007-01-01
The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex (or even uniformly convex). We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.
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.
Algorithms in nature: the convergence of systems biology and computational thinking.
Navlakha, Saket; Bar-Joseph, Ziv
2011-11-08
Computer science and biology have enjoyed a long and fruitful relationship for decades. Biologists rely on computational methods to analyze and integrate large data sets, while several computational methods were inspired by the high-level design principles of biological systems. Recently, these two directions have been converging. In this review, we argue that thinking computationally about biological processes may lead to more accurate models, which in turn can be used to improve the design of algorithms. We discuss the similar mechanisms and requirements shared by computational and biological processes and then present several recent studies that apply this joint analysis strategy to problems related to coordination, network analysis, and tracking and vision. We also discuss additional biological processes that can be studied in a similar manner and link them to potential computational problems. With the rapid accumulation of data detailing the inner workings of biological systems, we expect this direction of coupling biological and computational studies to greatly expand in the future.
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.
Regularization and Iterative Methods for Monotone Variational Inequalities
Directory of Open Access Journals (Sweden)
Xiubin Xu
2010-01-01
Full Text Available We provide a general regularization method for monotone variational inequalities, where the regularizer is a Lipschitz continuous and strongly monotone operator. We also introduce an iterative method as discretization of the regularization method. We prove that both regularization and iterative methods converge in norm.
Cruz, Pedro
2011-01-01
It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step increases or decreases if the scalar product of two subsequente increments of the estimates is positive or negative. This rule is intended to accelerate the entrance in the `stochastic behaviour' when initial conditions cause the algorithm to behave in a `deterministic fashion' for the starting iterations.
Gu, Ming; Wu, Cinna Julie
2009-01-01
In this article we propose an algorithm, PARNES, for the basis pursuit denoise problem which approximately finds a minimum one-norm solution to an underdetermined least squares problem. PARNES, (1) combines what we think are the best features of currently available methods SPGL1 and NESTA, and (2) incorporates a new improvement that exhibits linear convergence under the assumption of the restricted isometry property (RIP). As with SPGL1, our approach 'probes the Pareto frontier' and determines a solution to the BPDN problem by exploiting its relation between the LASSO problem as given by their Pareto curve. As with NESTA we rely on the accelerated proximal gradient method proposed by Yu. Nesterov that takes a remarkable O((L/e)^1/2) iterations to come within e > 0 of the optimal value, where L is the Lipschitz constant of the gradient of the objective function. Furthermore we introduce an 'outer loop' that regularly updates the prox center. Nesterov's accelerated proximal gradient method then becomes the 'inn...
A monotonic archive for pareto-coevolution.
de Jong, Edwin D
2007-01-01
Coevolution has already produced promising results, but its dynamic evaluation can lead to a variety of problems that prevent most algorithms from progressing monotonically. An important open question therefore is how progress towards a chosen solution concept can be achieved. A general solution concept for coevolution is obtained by viewing opponents or tests as objectives. In this setup known as Pareto-coevolution, the desired solution is the Pareto-optimal set. We present an archive that guarantees monotonicity for this solution concept. The algorithm is called the Incremental Pareto-Coevolution Archive (IPCA), and is based on Evolutionary Multi-Objective Optimization (EMOO). By virtue of its monotonicity, IPCA avoids regress even when combined with a highly explorative generator. This capacity is demonstrated on a challenging test problem requiring both exploration and reliability. IPCA maintains a highly specific selection of tests, but the size of the test archive nonetheless grows unboundedly. We therefore furthermore investigate how archive sizes may be limited while still providing approximate reliability. The LAyered Pareto-Coevolution Archive (LAPCA) maintains a limited number of layers of candidate solutions and tests, and thereby permits a trade-off between archive size and reliability. The algorithm is compared in experiments, and found to be more efficient than IPCA. The work demonstrates how the approximation of a monotonic algorithm can lead to algorithms that are sufficiently reliable in practice while offering better efficiency.
The regularized monotonicity method: detecting irregular indefinite inclusions
DEFF Research Database (Denmark)
Garde, Henrik; Staboulis, Stratos
2017-01-01
In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet map. Only few reconstruction methods apply when detecting indefinite...... of approximative measurement models, including the Complete Electrode Model, hence making the method robust against modelling error and noise. In particular, we demonstrate that for a convergent family of approximative models there exists a sequence of regularization parameters such that the outer shape...... of the inclusions is asymptotically exactly characterized. Finally, a peeling-type reconstruction algorithm is presented and, for the first time in literature, numerical examples of monotonicity reconstructions for indefinite inclusions are presented....
PPA BASED PREDICTION-CORRECTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
He Bingsheng; Jiang Jianlin; Qian Maijian; Xu Ya
2005-01-01
In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.
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.
Institute of Scientific and Technical Information of China (English)
Yuchao TANG; Chuanxi ZHU
2013-01-01
The purpose of this paper is to investigate the problem of finding a common fixed point of Lipschitz mappings.We introduce a multistep Ishikawa iteration approximation method which is based upon the Ishikawa iteration method and the Noor iteration method,and we prove some necessary and sufficient conditions for the strong convergence of the iteration scheme to a common fixed point of a finite family of quasi-Lipschitz mappings and pseudocontractive mappings,respectively.In particular,we establish a strong convergence theorem of the sequence generated by the multistep Ishikawa scheme to a common fixed point of nonexpansive mappings.As applications,some numerical experiments of the multistep Ishikawa iteration algorithm are given to demonstrate the convergence results.
Competitive learning of monotone Boolean functions
2014-01-01
We apply competitive analysis onto the problem of minimizing the number of queries to an oracle to completely reconstruct a given monotone Boolean function. Besides lower and upper bounds on the competitivity we determine optimal deterministic online algorithms for the smallest problem instances.
Classification Trees for Problems with Monotonicity Constraints
R. Potharst (Rob); A.J. Feelders
2002-01-01
textabstractFor classification problems with ordinal attributes very often the class attribute should increase with each or some of the explaining attributes. These are called classification problems with monotonicity constraints. Classical decision tree algorithms such as CART or C4.5 generally do
Institute of Scientific and Technical Information of China (English)
Yunjuan WANG; Detong ZHU
2008-01-01
Based on a differentiable merit function proposed by Taji et al.in "Math.Prog. Stud.,58,1993,369-383",the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints.By using the eigensystem decomposition and affine scaling mapping,the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem.Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.
Institute of Scientific and Technical Information of China (English)
张茁生; 刘贵忠; 刘峰
2003-01-01
A new algorithm for reconstructing a signal from its wavelet transform modulus maxima is presented based on an iterative method for solutions to monotone operator equations in Hilbert spaces. The algorithm's convergence is proved. Numerical simulations for different types of signals are given. The results indicate that compared with Mallat's alternate projection method, the proposed algorithm is sim-pler, faster and more effective.
Algorithms for unweighted least-squares factor analysis
Krijnen, WP
Estimation of the factor model by unweighted least squares (ULS) is distribution free, yields consistent estimates, and is computationally fast if the Minimum Residuals (MinRes) algorithm is employed, MinRes algorithms produce a converging sequence of monotonically decreasing ULS function values.
Convergence analysis of artificial bee colony algorithm%人工蜂群算法的收敛性分析
Institute of Scientific and Technical Information of China (English)
宁爱平; 张雪英
2013-01-01
The convergence of artificial bee colony algorithm is analyzed theoretically by using the stochastic process theory. Some mathematical definitions of artificial bee colony algorithm and one step transition probability of nectar source position are given and the Markov chain model of the algorithm is established. Some properties of the Markov chain are analyzed, and the conclusions that the artificial bee colony state sequence is a finite homogeneous of Markov chain and the state space of artificial bee colony is irreducible are obtained. It is proved that the artificial bee colony algorithm ensures the global convergence as the algorithm meets two assumptions of the random search algorithm for the global convergence.%利用随机过程理论，对人工蜂群算法收敛性进行理论分析，给出人工蜂群算法的一些数学定义和蜜源位置的一步转移概率，建立人工蜂群算法的Markov链模型，分析此Markov链的一些性质，论证了人工蜂群状态序列是有限齐次Markov链，且状态空间是不可约的。结合随机搜索算法的全局收敛准则，证明了人工蜂群算法能够满足随机搜索算法全局收敛的两个假设，保证算法的全局收敛。
On the sample monotonization problem
Takhanov, R. S.
2010-07-01
The problem of finding a maximal subsample in a training sample consisting of the pairs “object-answer” that does not violate monotonicity constraints is considered. It is proved that this problem is NP-hard and that it is equivalent to the problem of finding a maximum independent set in special directed graphs. Practically important cases in which a partial order specified on the set of answers is a complete order or has dimension two are considered in detail. It is shown that the second case is reduced to the maximization of a quadratic convex function on a convex set. For this case, an approximate polynomial algorithm based on linear programming theory is proposed.
Constructive techniques for zeros of monotone mappings in certain Banach spaces.
Diop, C; Sow, T M M; Djitte, N; Chidume, C E
2015-01-01
Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text]where J is the normalized duality mapping from E into [Formula: see text] and [Formula: see text] is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that [Formula: see text] converges strongly to the unique point [Formula: see text] Finally, our theorems are applied to the convex minimization problem.
Improved selection in totally monotone arrays
Energy Technology Data Exchange (ETDEWEB)
Mansour, Y. (Harvard Univ., Cambridge, MA (United States). Aiken Computation Lab.); Park, J.K. (Sandia National Labs., Albuquerque, NM (United States)); Schieber, B. (International Business Machines Corp., Yorktown Heights, NY (United States). Thomas J. Watson Research Center); Sen, S. (AT and T Bell Labs., Murray Hill, NJ (United States))
1991-01-01
This paper's main result is an O(({radical}{bar m}lgm)(n lg n) + mlg n)-time algorithm for computing the kth smallest entry in each row of an m {times} n totally monotone array. (A two-dimensional A = a(i,j) is totally monotone if for all i{sub 1} < i{sub 2} and j{sub 1} < j{sup 2}, < a(i{sub 1},j{sub 2}) implies a(i{sub 2},j{sub 1})). For large values of k (in particular, for k=(n/2)), this algorithm is significantly faster than the O(k(m+n))-time algorithm for the same problem due to Kravets and Park. An immediate consequence of this result is an O(n{sup 3/2} lg{sup 2}n)-time algorithm for computing the kth nearest neighbor of each vertex of a convex n-gon. In addition to the main result, we also give an O(n lg m)-time algorithm for computing an approximate median in each row of an m {times} n totally monotone array; this approximate median is an entry whose rank in its row lies between (n/4) and (3n/4) {minus} 1. 20 refs., 3 figs.
Guionnet, A
2012-01-01
By solving a free analog of the Monge-Amp\\`ere equation, we prove a non-commutative analog of Brenier's monotone transport theorem: if an $n$-tuple of self-adjoint non-commutative random variables $Z_{1},...,Z_{n}$ satisfies a regularity condition (its conjugate variables $\\xi_{1},...,\\xi_{n}$ should be analytic in $Z_{1},...,Z_{n}$ and $\\xi_{j}$ should be close to $Z_{j}$ in a certain analytic norm), then there exist invertible non-commutative functions $F_{j}$ of an $n$-tuple of semicircular variables $S_{1},...,S_{n}$, so that $Z_{j}=F_{j}(S_{1},...,S_{n})$. Moreover, $F_{j}$ can be chosen to be monotone, in the sense that $F_{j}=\\mathscr{D}_{j}g$ and $g$ is a non-commutative function with a positive definite Hessian. In particular, we can deduce that $C^{*}(Z_{1},...,Z_{n})\\cong C^{*}(S_{1},...,S_{n})$ and $W^{*}(Z_{1},...,Z_{n})\\cong L(\\mathbb{F}(n))$. Thus our condition is a useful way to recognize when an $n$-tuple of operators generate a free group factor. We obtain as a consequence that the q-deforme...
Directory of Open Access Journals (Sweden)
Pongsakorn Sunthrayuth
2012-01-01
Full Text Available We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others.
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...
Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms
Khardon, R; Servedio, R A; 10.1613/jair.1655
2011-01-01
The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses in this context is to expand the feature set to include conjunctions of basic features. This can be done explicitly or where possible by using a kernel function. Focusing on the well known Perceptron and Winnow algorithms, the paper demonstrates a tradeoff between the computational efficiency with which the algorithm can be run over the expanded feature space and the generalization ability of the corresponding learning algorithm. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Perceptron algorithm over a feature space of exponentially many conjunctions; however we also show that using such kernels, the Perceptron algorithm can provably make an ex...
Directory of Open Access Journals (Sweden)
Shenghua Wang
2013-01-01
Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.
Directory of Open Access Journals (Sweden)
Yunrui Guo
2008-09-01
Full Text Available The purpose of this paper is to study the strong convergence of a modified iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a relaxed cocoercive mapping, as well as the set of solutions of a mixed-equilibrium problem. Our results extend recent results of Takahashi and Takahashi (2007, Marino and Xu (2006, Combettes and Hirstoaga (2005, Iiduka and Takahashi (2005, and many others.
Directory of Open Access Journals (Sweden)
Gao Xueliang
2008-01-01
Full Text Available Abstract The purpose of this paper is to study the strong convergence of a modified iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a relaxed cocoercive mapping, as well as the set of solutions of a mixed-equilibrium problem. Our results extend recent results of Takahashi and Takahashi (2007, Marino and Xu (2006, Combettes and Hirstoaga (2005, Iiduka and Takahashi (2005, and many others.
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...... adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography (image reconstruction from projections)....
MONOTONE ITERATION FOR ELLIPTIC PDEs WITH DISCONTINUOUS NONLINEAR TERMS
Institute of Scientific and Technical Information of China (English)
Zou Qingsong
2005-01-01
In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.
Edit Distance to Monotonicity in Sliding Windows
Chan, Ho-Leung; Lee, Lap-Kei; Pan, Jiangwei; Ting, Hing-Fung; Zhang, Qin
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 data stream is becoming well-understood over the past few years. Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the $w$ most recent items in the stream for any $w \\ge 1$. We give a deterministic algorithm which can return an estimate within a factor of $(4+\\eps)$ using $O(\\frac{1}{\\eps^2} \\log^2(\\eps w))$ space. We also extend the study in two directions. First, we consider a stream where each item is associated with a value from a partial ordered set. We give a randomized $(4+\\epsilon)$-approximate algorithm using $O(\\frac{1}{\\epsilon^2} \\log \\epsilon^2 w \\log w)$ space. Second, we consider an out-of-order strea...
并行模糊系统的预测和辨识收敛性%Prediction and Identification Algorithm Convergence of Parallel Fuzzy Systems
Institute of Scientific and Technical Information of China (English)
於东军; 杨静宇
2002-01-01
Fuzzy systems can be used to identify nonlinear dynamic systems in two modes. One is series-parallel modeand the other is parallel mode. The prediction and identification algorithm convergence of nonlinear dynamic system i-dentification using parallel fuzzy systems is discussed in this paper. It is proved that as long as the parameters of par-allel fuzzy systems meet some prerequisites, the parallel prediction procedure converges and the parallel identificationalgorithm locally converges. This conclusion has instructive significance for parallel fuzzy systems' application.
Symmetric Workpiece Localization Algorithms: Convergence and Improvements%对称工件定位算法:收敛性及其改进
Institute of Scientific and Technical Information of China (English)
陈善勇; 李圣怡; 戴一帆
2006-01-01
Symmetric workpiece localization algorithms combine alternating optimization and linearization. The iterative variables are partitioned into two groups. Then simple optimization approaches can be employed for each subset of variables, where optimization of configuration variables is simplified as a linear least-squares problem (LSP). Convergence of current symmetric localization algorithms is discussed firstly. It is shown that simply taking the solution of the LSP as start of the next iteration may result in divergence or incorrect convergence. Therefore in our enhanced algorithms, line search is performed along the solution of the LSP in order to find a better point reducing the value of objective function. We choose this point as start of the next iteration. Better convergence is verified by numerical simulation. Besides, imposing boundary constraints on the LSP proves to be another efficient way.
On Convergence of the Nelder-Mead Simplex Algorithm for Unconstrained Stochastic Optimization
1995-05-01
the best point. Reklaitis , Ravindran, and Ragsdell (1983) further classify direct-search methods into two classes: heuristic techniques and...restricted conditions" ( Reklaitis et al., 1983, p. 75). The Nelder-Mead algorithm is a heuristic direct-search method. An example of a theoretically...Pressure Liquid Cliromatography. Analytica Clumica Ada, 93, 211-219. Reklaitis , G. V., Ravindran, A., & Ragsdell, K. M. (1983). Engineering
Reem, Daniel; De Pierro, Alvaro
2017-04-01
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed inexact versions of several accelerated proximal methods aiming at solving this minimization problem. This paper shows that inexact versions of a method of Beck and Teboulle (fast iterative shrinkable tresholding algorithm) preserve, in a Hilbert space setting, the same (non-asymptotic) rate of convergence under some assumptions on the decay rate of the error terms The notion of inexactness discussed here seems to be rather simple, but, interestingly, when comparing to related works, closely related decay rates of the errors terms yield closely related convergence rates. The derivation sheds some light on the somewhat mysterious origin of some parameters which appear in various accelerated methods. A consequence of the analysis is that the accelerated method is perturbation resilient, making it suitable, in principle, for the superiorization methodology. By taking this into account, we re-examine the superiorization methodology and significantly extend its scope. This work was supported by FAPESP 2013/19504-9. The second author was supported also by CNPq grant 306030/2014-4.
A Neurodynamic Model to Solve Nonlinear Pseudo-Monotone Projection Equation and Its Applications.
Eshaghnezhad, Mohammad; Effati, Sohrab; Mansoori, Amin
2016-09-29
In this paper, a neurodynamic model is given to solve nonlinear pseudo-monotone projection equation. Under pseudo-monotonicity condition and Lipschitz continuous condition, the projection neurodynamic model is proved to be stable in the sense of Lyapunov, globally convergent, globally asymptotically stable, and globally exponentially stable. Also, we show that, our new neurodynamic model is effective to solve the nonconvex optimization problems. Moreover, since monotonicity is a special case of pseudo-monotonicity and also since a co-coercive mapping is Lipschitz continuous and monotone, and a strongly pseudo-monotone mapping is pseudo-monotone, the neurodynamic model can be applied to solve a broader classes of constrained optimization problems related to variational inequalities, pseudo-convex optimization problem, linear and nonlinear complementarity problems, and linear and convex quadratic programming problems. Finally, several illustrative examples are stated to demonstrate the effectiveness and efficiency of our new neurodynamic model.
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes
Norde, H.W.; Moretti, S.; Tijs, S.H.
2001-01-01
In this paper we present the Subtraction Algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme.As a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegati
Chuang, Ching-Cheng; Tsai, Jui-che; Chen, Chung-Ming; Yu, Zong-Han; Sun, Chia-Wei
2012-04-01
Diffuse optical tomography (DOT) is an emerging technique for functional biological imaging. The imaging quality of DOT depends on the imaging reconstruction algorithm. The SIRT has been widely used for DOT image reconstruction but there is no criterion to truncate based on any kind of residual parameter. The iteration loops will always be decided by experimental rule. This work presents the CR calculation that can be great help for SIRT optimization. In this paper, four inhomogeneities with various shapes of absorption distributions are simulated as imaging targets. The images are reconstructed and analyzed based on the simultaneous iterative reconstruction technique (SIRT) method. For optimization between time consumption and imaging accuracy in reconstruction process, the numbers of iteration loop needed to be optimized with a criterion in algorithm, that is, the root mean square error (RMSE) should be minimized in limited iterations. For clinical applications of DOT, the RMSE cannot be obtained because the measured targets are unknown. Thus, the correlations between the RMSE and the convergence rate (CR) in SIRT algorithm are analyzed in this paper. From the simulation results, the parameter CR reveals the related RMSE value of reconstructed images. The CR calculation offers an optimized criterion of iteration process in SIRT algorithm for DOT imaging. Based on the result, the SIRT can be modified with CR calculation for self-optimization. CR reveals an indicator of SIRT image reconstruction in clinical DOT measurement. Based on the comparison result between RMSE and CR, a threshold value of CR (CRT) can offer an optimized number of iteration steps for DOT image reconstruction. This paper shows the feasibility study by utilizing CR criterion for SIRT in simulation and the clinical application of DOT measurement relies on further investigation.
Monotone partitions and almost partitions
Bonanzinga, M.; Cammaroto, F.; van Mill, J.; Pansera, B.A.
2014-01-01
In this paper we are interested in monotone versions of partitionability of topological spaces and weak versions thereof. We identify several classes of spaces with these properties by constructing trees of open sets with various properties.
Pulliam, T. H.; Steger, J. L.
1985-01-01
In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.
Directory of Open Access Journals (Sweden)
Feng Gu
2012-01-01
Full Text Available The purpose of this paper is to establish a strong convergence of a new parallel iterative algorithm with mean errors to a common fixed point for two finite families of Ćirić quasi-contractive operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of Berinde, Gu, Rafiq, Rhoades, and Zamfirescu.
Why Monotonous Repetition is Unsatisfying
Salingaros, Nikos A
2011-01-01
Human beings prefer ordered complexity and not randomness in their environment, a result of our perceptual system evolving to interpret natural forms. We also recognize monotonously repeating forms as unnatural. Although widespread in today's built environment, such forms generate reactions ranging from boredom to unease. Christopher Alexander has introduced rules for generating forms adapted to natural geometries, which show structured variation with multiple symmetries in a hierarchy of scales. It turns out to be impossible to generate monotonously repeating forms by following those rules. As it is highly probable that traditional artifacts, buildings, and cities were created instinctively using a version of the same rules, this is the reason we never find monotonously repeating forms in traditional cultures.
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...... (with at least three members) and its participation constraint if and only if the aggregate income to that coalition is always maximized. An impossibility result demonstrates that there is no welfare maximizing allocation method in which agents' individual incomes monotonically increase in society......'s income. Thus, for any such allocation method, there are situations where some agents have incentives to prevent society in becoming richer....
Stability and monotonicity of Lotka-Volterra type operators
Mukhamedov, Farrukh
2009-01-01
In the present paper, we study Lotka-Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. After, we introduce a new class of LV-type operators, called $M$LV type. We prove convergence of their trajectories and study certain its properties. Moreover, we show that such kind of operators have totaly different behavior than ${\\mathbf{f}}$-monotone LV type operators.
Energy Technology Data Exchange (ETDEWEB)
Paszkowicz, Wojciech [Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, PL-02-668 Warsaw (Poland)]. E-mail: paszk@ifpan.edu.pl
2006-04-27
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.
A Characterization of Generalized Monotone Normed Cones
Institute of Scientific and Technical Information of China (English)
S.ROMAGUERA; E.A.S(A)NCHEZ-P(E)REZ; O.VALERO
2007-01-01
Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple (C, p) as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi-normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone.We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.
Guermond, Jean-Luc
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.
Testing Monotonicity of Pricing Kernels
Timofeev, Roman
2007-01-01
In this master thesis a mechanism to test mononicity of empirical pricing kernels (EPK) is presented. By testing monotonicity of pricing kernel we can determine whether utility function is concave or not. Strictly decreasing pricing kernel corresponds to concave utility function while non-decreasing EPK means that utility function contains some non-concave regions. Risk averse behavior is usually described by concave utility function and considered to be a cornerstone of classical behavioral ...
Institute of Scientific and Technical Information of China (English)
崔蒙蒙; 凌晨
2014-01-01
非精确Levenberg-Marquardt（L-M）算法是求解非光滑约束方程组的重要算法之一。在将非光滑约束方程组等价转化成无约束方程的基础上，该文针对一种新的非精确光滑化L-M算法，在局部误差界条件下，得到此算法具有超线性或二次收敛性质。%The inexact Levenberg-Marquardt ( L-M) algorithm is one of the important algorithms for solving nonsmooth constraint equations .Based upon the unconstrained reformulation of the original problem , a new inexact smoothing L-M algorithm is presented .And under the local error bound condition , this algorithm enjoys the local superlinear or quadratic rate of convergence .
Monotone data visualization using rational trigonometric spline interpolation.
Ibraheem, Farheen; Hussain, Maria; Hussain, Malik Zawwar
2014-01-01
Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Monotone Data Visualization Using Rational Trigonometric Spline Interpolation
Directory of Open Access Journals (Sweden)
Farheen Ibraheem
2014-01-01
Full Text Available Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Monotonicity of chi-square test statistics
Ryu, Keunkwan
2003-01-01
This paper establishes monotonicity of the chi-square test statistic. As the more efficient parameter estimator is plugged into the test statistic, the degrees of freedom of the resulting chi-square test statistic monotonically increase.
Adaptive genetic algorithm with the criterion of premature convergence%具有成熟前收敛判断的自适应遗传算法
Institute of Scientific and Technical Information of China (English)
袁晓辉; 曹玲; 夏良正
2003-01-01
针对传统的简单遗传算法的缺陷,提出了改进的具有成熟前收敛判断的自适应遗传算法.用群体熵值和均方差来预报成熟前收敛的发生.当成熟前收敛发生时 ,提出以群体中的最优个体为基础,在其一定大小领域内随机产生若干个体,取代原种群中的部分个体,其中更新的个体数占群体中个体总数的30%～40%,领域大小与目标函数极值点分布有关.仿真实验证明,算法的收敛速度和全局收敛概率都有显著的提高.%To counter the defect of traditional genetic algorithms, an improved adaptive genetic algorithm with the criterion of premature convergence is provided. The oc currence of premature convergence is forecasted using colony entropy and colony variance. When premature convergence occurs, new individuals are generat ed in proper scale randomly based on superior individuals in the colony. We use these new individuals to replace some individuals in the old colony. The update d individuals account for 30%-40% of all individuals and the size of scale is re lated to the distribution of the extreme value of the target function. Simulation tests show that there is much improvement in the speed of convergence and the probability of global convergence.
Some Generalizations of Monotonicity Condition and Applications
Institute of Scientific and Technical Information of China (English)
虞旦盛; 周颂平
2006-01-01
@@ O Introduction It is well known that there are a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc..
Three penalized EM-type algorithms for PET image reconstruction.
Teng, Yueyang; Zhang, Tie
2012-06-01
Based on Bayes theory, Green introduced the maximum a posteriori (MAP) algorithm to obtain a smoothing reconstruction for positron emission tomography. This algorithm is flexible and convenient for most of the penalties, but it is hard to guarantee convergence. For a common goal, Fessler penalized a weighted least squares (WLS) estimator by a quadratic penalty and then solved it with the successive over-relaxation (SOR) algorithm, however, the algorithm was time-consuming and difficultly parallelized. Anderson proposed another WLS estimator for faster convergence, on which there were few regularization methods studied. For three regularized estimators above, we develop three new expectation maximization (EM) type algorithms to solve them. Unlike MAP and SOR, the proposed algorithms yield update rules by minimizing the auxiliary functions constructed on the previous iterations, which ensure the cost functions monotonically decreasing. Experimental results demonstrated the robustness and effectiveness of the proposed algorithms.
Computation of Optimal Monotonicity Preserving General Linear Methods
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.
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.
DEFF Research Database (Denmark)
Nielson, Hanne Riis; Nielson, Flemming
2009-01-01
The calculus of communicating systems, CCS, was introduced by Robin Milner as a calculus for modelling concurrent systems. Subsequently several techniques have been developed for analysing such models in order to get further insight into their dynamic behaviour. In this paper we present a static...... analysis for approximating the control structure embedded within the models. We formulate the analysis as an instance of a monotone framework and thus draw on techniques that often are associated with the efficient implementation of classical imperative programming languages. We show how to construct...
Institute of Scientific and Technical Information of China (English)
程晓良; 徐渊辑; 孟炳泉
2005-01-01
An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed.The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence.The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved.Some numerical examples are presented to confirm the effciency of this algorithm.
Approximations for Monotone and Non-monotone Submodular Maximization with Knapsack Constraints
Kulik, Ariel; Tamir, Tami
2011-01-01
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we consider the problem of maximizing any submodular function subject to $d$ knapsack constraints, where $d$ is a fixed constant. We establish a strong relation between the discrete problem and its continuous relaxation, obtained through {\\em extension by expectation} of the submodular function. Formally, we show that, for any non-negative submodular function, an $\\alpha$-approximation algorithm for the continuous relaxation implies a randomized $(\\alpha - \\eps)$-approximation algorithm for the discrete problem. We use this relation to improve the best known approximation ratio for the problem to $1/4- \\eps$, for any $\\eps > 0$, and to obtain a nearly optimal $(1-e^{-1}-\\eps)-$approximation ratio for the monotone case, for any $\\eps>0$. We further show that the probabilistic domain ...
一种快速收敛的自适应蚁群算法%Investigation on a Fast Convergent Adaptive Ant Colony Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
潘伟强; 李长云; 胡盛龙
2012-01-01
The ant colony optimization has deficiencies of slow convergence speed and difficult parameters selection.By analyzing the parameters'effect on the algorithm and comparing multiple parameter optimization methods,adopts the hybrid algorithm of particle swarm optimization and ant colony optimization to optimize parameters,and proposes a fast convergent adaptive ant colony optimization.The simulation of the traveling salesman problem shows that the algorithm is feasible and effective.%针对蚁群算法收敛速度慢、参数选择难的不足,通过分析各参数对算法的影响和比较多种参数寻优方法,采用粒子群算法对蚁群算法进行参数寻优,并提出了一种快速收敛的自适应蚁群算法。针对旅行商问题的仿真试验表明,该算法是可行且有效的。
Global convergence property of a class of non-quasi-Newton algorithms%一类非拟牛顿算法的全局收敛性
Institute of Scientific and Technical Information of China (English)
张长海; 王玉学; 张立凡; 张军
2001-01-01
In this paper, under some conditions, we prove the global convergence property of a class of non-quasi-Newton algorithms for uncontrained optimization problems with Goldstein line search on uniformly convex objective function.%在一定条件下，对于一致凸的目标函数，证明了带有Goldstein线搜索的无约束最优化问题的一类非拟牛顿算法的全局收敛性.
A novel complex-system-view-based method for system effectiveness analysis: Monotonic indexes space
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on the characteristics of the complex system, this paper presents a novel method, the monotonic indexes space method, for the effectiveness analysis of the complex system. First, it presents some basic concepts and assumption such as the monotonic indexes space, monotonic indexes requirement locus, etc. Second, based on the assumption that indexes are monotonic for the requirements, an algorithm is proposed and applied to numerical approximation of monotonic indexes requirement locus with hyperboxes. Third, this paper proposes two algorithms for acquiring intersection of several monotonic indexes requirement locus. Fourth, this paper proposes the monotonic-index- space based system analysis model such as the system evaluation model, the sensitivity analysis model for indexes. Based on the practical requirement, the concept of fuzzy monotonic indexes requirement locus and the corresponding analysis model are introduced. Finally, this paper applies the above-mentioned models to analyze the effectiveness of a notional anti-stealth-air-defense information system. And the outputs show that the method is promising.
Nonparametric estimation for hazard rate monotonously decreasing system
Institute of Scientific and Technical Information of China (English)
Han Fengyan; Li Weisong
2005-01-01
Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.
Deterministic homogenization of parabolic monotone operators with time dependent coefficients
Directory of Open Access Journals (Sweden)
Gabriel Nguetseng
2004-06-01
Full Text Available We study, beyond the classical periodic setting, the homogenization of linear and nonlinear parabolic differential equations associated with monotone operators. The usual periodicity hypothesis is here substituted by an abstract deterministic assumption characterized by a great relaxation of the time behaviour. Our main tool is the recent theory of homogenization structures by the first author, and our homogenization approach falls under the two-scale convergence method. Various concrete examples are worked out with a view to pointing out the wide scope of our approach and bringing the role of homogenization structures to light.
Reem, Daniel
2015-01-01
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed inexact versions of several accelerated proximal methods aiming at solving this minimization problem. This paper shows that inexact versions of a method of Beck and Teboulle (FISTA) preserve, in a Hilbert space setting, the same (non-asymptotic) rate of convergence under some assumptions on the decay rate of the error terms. The notion of inexactness discussed here seems to be rather simple, but, interestingly, when comparing to related works, similar decay rates of the errors terms yield similar convergence rates. The derivation sheds some light on the somewhat mysterious origin of some parameters which appear in various accelerated methods. A consequence of the analysis is that the accelerated method is perturbation resilient, making it suitable, in principle, for the super...
Directory of Open Access Journals (Sweden)
Wang Zhenhua
2015-02-01
Full Text Available To improve the computational efficiency and hold calculation accuracy at the same time, we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method (DOM and the spatial domain decomposition parallelization (DDP are combined by message passing interface (MPI language. The DDP–DOM computation of the radiation heat transfer within the rectangular furnace is described. When the result of DDP–DOM along one-dimensional direction is compared with that along multi-dimensional directions, it is found that the result of the latter one has higher precision without considering the medium scattering. Meanwhile, an in-depth study of the convergence of DDP–DOM for radiation heat transfer is made. Analyzing the cause of the weak convergence, we relate the total number of iteration steps when the convergence is obtained to the number of sub-domains. When we decompose the spatial domain along one-, two- and three-dimensional directions, different linear relationships between the number of total iteration steps and the number of sub-domains will be possessed separately, then several equations are developed to show the relationships. Using the equations, some phenomena in DDP–DOM can be made clear easily. At the same time, the correctness of the equations is verified.
ON NEURAL NETWORK BASED ON THREE CONVERGENCES LM ALGORITHM%基于三次收敛LM算法的神经网络研究
Institute of Scientific and Technical Information of China (English)
郭秀才; 尚赛花
2014-01-01
为了解决传统神经网络实际应用中计算复杂、耗时过长等问题，在LM（Levenberg-Marquardt）算法的基础上，结合数学最优化理论，找出三次收敛的改进型LM算法，且将其应用于BP神经网络。利用一组火灾现场数据，通过Matlab仿真对改进型LMBP算法和标准LMBP算法从收敛时间和仿真曲线拟合度两方面进行比较。结果表明改进型LMBP算法在收敛时间和拟合度两方面都有更好的效果，且该算法具有一般性，可以通过获取国民生产中各种应用场景的样本，采用该算法进行预测，更好地指导生产。%In order to solve the practical problems of traditional neural network application in computation complexity and long time consu-ming,on the basis of LM algorithm and combined with mathematical optimisation theory,we find out the improved LM algorithm with three convergences and apply it to BP neural network.Moreover,by using a set of data got from the scene of the fire,we compare the improved LMBP algorithm and the standard LMBP algorithm through Matlab simulation in two aspects of convergence time and simulation curve fitting. Experiments show that the improved LMBP algorithm has better effect than the standard LMBP algorithm in these two aspects.The improved LMBP algorithm also has the generality,it can be used to predict for better guiding the production by obtaining the samples of various scenari-os in national product.
Institute of Scientific and Technical Information of China (English)
童小娇; 周叔子
2003-01-01
This paper presents a trust region two-phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
Wang, L.; Wang, T. G.; Wu, J. H.; Cheng, G. P.
2016-09-01
A novel multi-objective optimization algorithm incorporating evolution strategies and vector mechanisms, referred as VD-MOEA, is proposed and applied in aerodynamic- structural integrated design of wind turbine blade. In the algorithm, a set of uniformly distributed vectors is constructed to guide population in moving forward to the Pareto front rapidly and maintain population diversity with high efficiency. For example, two- and three- objective designs of 1.5MW wind turbine blade are subsequently carried out for the optimization objectives of maximum annual energy production, minimum blade mass, and minimum extreme root thrust. The results show that the Pareto optimal solutions can be obtained in one single simulation run and uniformly distributed in the objective space, maximally maintaining the population diversity. In comparison to conventional evolution algorithms, VD-MOEA displays dramatic improvement of algorithm performance in both convergence and diversity preservation for handling complex problems of multi-variables, multi-objectives and multi-constraints. This provides a reliable high-performance optimization approach for the aerodynamic-structural integrated design of wind turbine blade.
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.
Monotonic Allocation Schemes in Clan Games
Voorneveld, M.; Tijs, S.H.; Grahn, S.
2000-01-01
Total clan games are characterized using monotonicity, veto power of the clan members, and a concavity condition reflecting the decreasing marginal contribution of non-clan members to growing coalitions.This decreasing marginal contribution is incorporated in the notion of a bi-monotonic allocation
Monotone models for prediction in data mining
Velikova, M.V.
2006-01-01
This dissertation studies the incorporation of monotonicity constraints as a type of domain knowledge into a data mining process. Monotonicity constraints are enforced at two stages¿data preparation and data modeling. The main contributions of the research are a novel procedure to test the degree of
Monotonic Stable Solutions for Minimum Coloring Games
Hamers, H.J.M.; Miquel, S.; Norde, H.W.
2011-01-01
For the class of minimum coloring games (introduced by Deng et al. (1999)) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont (1990)). We show that a minimum coloring game on a graph G has a population monotonic allocation scheme if and only if G is (P4,
Monotonicity-preserving linear multistep methods
Hundsdorfer, W.; Ruuth, S.J.; Spiteri, R.J.
2002-01-01
In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total-variation-bounded (TVB) property
Version Spaces and Generalized Monotone Boolean Functions
J.C. Bioch (Cor); T. Ibaraki
2002-01-01
textabstractWe consider generalized monotone functions f: X --> {0,1} defined for an arbitrary binary relation <= on X by the property x <= y implies f(x) <= f(y). These include the standard monotone (or positive) Boolean functions, regular Boolean functions and other interesting functions as speci
Version Spaces and Generalized Monotone Boolean Functions
J.C. Bioch (Cor); T. Ibaraki
2002-01-01
textabstractWe consider generalized monotone functions f: X --> {0,1} defined for an arbitrary binary relation <= on X by the property x <= y implies f(x) <= f(y). These include the standard monotone (or positive) Boolean functions, regular Boolean functions and other interesting functions as
Monotone Hurwitz numbers in genus zero
Goulden, I P; Novak, Jonathan
2012-01-01
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.
Pospelov, A. I.
2016-08-01
Adaptive methods for the polyhedral approximation of the convex Edgeworth-Pareto hull in multiobjective monotone integer optimization problems are proposed and studied. For these methods, theoretical convergence rate estimates with respect to the number of vertices are obtained. The estimates coincide in order with those for filling and augmentation H-methods intended for the approximation of nonsmooth convex compact bodies.
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.
Nguyen, Dinh-Liem; Klibanov, Michael V.; Nguyen, Loc H.; Kolesov, Aleksandr E.; Fiddy, Michael A.; Liu, Hui
2017-09-01
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. The challenges for the inverse problem under the consideration are not only from its high nonlinearity and severe ill-posedness but also from the facts that the amount of the measured data is minimal and that these raw data are contaminated by a significant amount of noise, due to a non-ideal experimental setup. This setup is motivated by our target application in detecting and identifying explosives. We show in this paper how the raw data can be preprocessed and successfully inverted using our inversion method. More precisely, we are able to reconstruct the dielectric constants and the locations of the scattering objects with a good accuracy, without using any advanced a priori knowledge of their physical and geometrical properties.
Viable harvest of monotone bioeconomic models
De Lara, Michel; Cabrera, Hector Ramirez
2009-01-01
Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomics dynamics in the presence of state and control constraints. In practice, these latter ``acceptable configurations'' represent production and preservation requirements to be satisfied for all time, and they also possess monotonicity properties. A state $\\state$ is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from $\\state$ and satisfying the constraints. Under monotonicity assumptions, we present upper and lower estimates of the viability kernel. This helps delineating domains where a viable management is possible. Numerical examples, in the context of fisheries management, for the Chilean sea bass (\\emph{Dissostichus eleginoides}) and Alfonsino (\\emph{Beryx splendens}) are given.
Hyperbolic monotonicity in the Hilbert ball
Directory of Open Access Journals (Sweden)
Reich Simeon
2006-01-01
Full Text Available We first characterize -monotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents.
Quasi-optimal convergence rate of an AFEM for quasi-linear problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2010-01-01
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and D\\"orfler's strategy is assumed for marking. We first prove a contraction property for a suitable definition of total error, which is equivalent to the total error as defined by Casc\\'on et al. (in SIAM J. Numer. Anal. 46 (2008), 2524--2550), and implies line...
... from convergence insufficiency? Symptoms of convergence insufficiency include diplopia (double vision) and headaches when reading. Many patients ... another time or simply watched for symptoms of diplopia or headaches with near work. A patient who ...
Solving the power flow equations: a monotone operator approach
Energy Technology Data Exchange (ETDEWEB)
Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-07-21
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial “guess” for the solution, which is always available in normal system operations. However, with the increase in levels of intermittent generation, the assumption of a good initial guess always being available is no longer valid. In this paper, we solve this problem using the theory of monotone operators. We show that it is possible to compute (using an offline optimization) a “monotonicity domain” in the space of voltage phasors. Given this domain, there is a simple efficient algorithm that will either find a solution in the domain, or provably certify that no solutions exist in it. We validate the approach on several IEEE test cases and demonstrate that the offline optimization can be performed tractably and the computed “monotonicity domain” includes all practically relevant power flow solutions.
Institute of Scientific and Technical Information of China (English)
张会; 张海; 勾明
2016-01-01
Compressive sensing based on SCAD has good theoretical properties for sparse signal reconstruction with noise. It is vital to study this kind of algorithms. The iterative thresholding algorithm is one of the most eﬃcient algorithms to solve the problem of com-pressed sensing. In this paper, we study the convergence of the iterative thresholding algorithm for compressive sensing based on SCAD. We give some suﬃcient conditions on the conver-gence of the iterative thresholding algorithm. We prove that the algorithm is convergent with exponentially decaying error. Furthermore, we study the convergence of an improved iterative thresholding SCAD algorithm based on an approximate message passing algorithm.%基于SCAD罚函数的压缩感知在有噪声稀疏信号重建中具有优良的理论及应用效果，开展其快速重建算法研究有着重要的意义，阈值迭代算法是解决压缩传感问题最有效的算法之一。本文研究了基于SCAD罚函数的压缩感知阈值迭代算法的收敛性问题，给出了算法收敛到稀疏解的充分条件，并证明了迭代估计值以指数阶速率收敛于最优值。进一步，本文给出了基于AMP改进的SCAD阈值迭代算法的收敛性分析。
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}.
Solving variational inequalities with Stochastic Mirror-Prox algorithm
Juditsky, Anatoli; Tauvel, Claire
2008-01-01
In this paper we consider iterative methods for stochastic variational inequalities (s.v.i.) with monotone operators. Our basic assumption is that the operator possesses both smooth and nonsmooth components. Further, only noisy observations of the problem data are available. We develop a novel Stochastic Mirror-Prox (SMP) algorithm for solving s.v.i. and show that with the convenient stepsize strategy it attains the optimal rates of convergence with respect to the problem parameters. We apply the SMP algorithm to Stochastic composite minimization and describe particular applications to Stochastic Semidefinite Feasability problem and Eigenvalue minimization.
Solving variational inequalities with stochastic mirror-prox algorithm
Directory of Open Access Journals (Sweden)
Anatoli B. Juditsky
2011-01-01
Full Text Available We consider iterative methods for stochastic variational inequalities (s.v.i. with monotone operators. Our basic assumption is that the operator possesses both smooth and nonsmooth components. Further, only noisy observations of the problem data are available. We develop a novel Stochastic Mirror-Prox (SMP algorithm for solving s.v.i. and show that with the convenient stepsize strategy it attains the optimal rates of convergence with respect to the problem parameters. We apply the SMP algorithm to Stochastic composite minimization and describe particular applications to Stochastic Semidefinite Feasability problem and Eigenvalue minimization.
Monotone Rank and Separations in Computational Complexity
Li, Yang D
2011-01-01
In the paper, we introduce the concept of monotone rank, and using it as a powerful tool, we obtain several important and strong separation results in computational complexity. We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to a longstanding open problem posed by Nisan \\cite{Nis1991} in algebraic complexity. More specifically, we exhibit a homogeneous algebraic function $f$ of degree $d$ ($d$ even) on $n$ variables with the monotone algebraic branching program (ABP) complexity $\\Omega(n^{d/2})$ and the non-monotone ABP complexity $O(d^2)$. We propose a relaxed version of the famous Bell's theorem\\cite{Bel1964}\\cite{CHSH1969}. Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics, and therefore is an impossibility result. Bell's theorem heavily relies on the diversity of the measurements. We prove that even if we fix the measurement, infinite amo...
The monotonic and fatigue behavior of CFCCs
Energy Technology Data Exchange (ETDEWEB)
Miriyala, N.; Liaw, P.K.; McHargue, C.J. [Univ. of Tennessee, Knoxville, TN (United States); Snead, L.L. [Oak Ridge National Laboratory, TN (United States)
1996-04-01
Flexure tests were performed to study the fabric orientation effects on the monotonic and fatigue behavior of two commercially available continuous fiber reinforced ceramic composites (CFCCs), namely (i) Nicalon fiber fabric reinforced alumina (Al{sub 2}O{sub 3}) matrix composite fabricated by a direct molten metal oxidation (DIMOX) process and, (ii) Nicalon fiber fabric reinforced silicon carbide (SiC) matrix composite fabricated by an isothermal chemical vapor infiltration (ICVI) process. The fabric orientation effects on the monotonic and fatigue behavior were strong in the Nicalon/Al{sub 2}O{sub 3} composite, while they were relatively weak in the Nicalon/SiC composite.
Weighted monotonicity inequalities for unbounded operators
Hoa, Dinh Trung
2011-01-01
Let $\\tau$ be a faithful normal semifinite trace on a von Neumann algebra $\\mathcal{M}$. For a continuous nonnegative convex monotone nondecreasing function $f$ on convex subset $\\Omega$ of $\\mathbb{R}$ and weight nonnegative Borel function $w$ we consider weighted monotonicity inequalities of the form {equation*} \\tau(w(A)^{1/2}f(A)w(A)^{1/2}) \\le \\tau (w(A)^{1/2}f(B)w(A)^{1/2}), {equation*} where $A$ and $B$ are unbounded operators affiliated with respect to algebra $\\mathcal{M}$.
Directory of Open Access Journals (Sweden)
Jaspreet Kaur
Full Text Available Fitting parameter sets of non-linear equations in cardiac single cell ionic models to reproduce experimental behavior is a time consuming process. The standard procedure is to adjust maximum channel conductances in ionic models to reproduce action potentials (APs recorded in isolated cells. However, vastly different sets of parameters can produce similar APs. Furthermore, even with an excellent AP match in case of single cell, tissue behaviour may be very different. We hypothesize that this uncertainty can be reduced by additionally fitting membrane resistance (Rm. To investigate the importance of Rm, we developed a genetic algorithm approach which incorporated Rm data calculated at a few points in the cycle, in addition to AP morphology. Performance was compared to a genetic algorithm using only AP morphology data. The optimal parameter sets and goodness of fit as computed by the different methods were compared. First, we fit an ionic model to itself, starting from a random parameter set. Next, we fit the AP of one ionic model to that of another. Finally, we fit an ionic model to experimentally recorded rabbit action potentials. Adding the extra objective (Rm, at a few voltages to the AP fit, lead to much better convergence. Typically, a smaller MSE (mean square error, defined as the average of the squared error between the target AP and AP that is to be fitted was achieved in one fifth of the number of generations compared to using only AP data. Importantly, the variability in fit parameters was also greatly reduced, with many parameters showing an order of magnitude decrease in variability. Adding Rm to the objective function improves the robustness of fitting, better preserving tissue level behavior, and should be incorporated.
Monotone Comparative Statics for the Industry Composition
DEFF Research Database (Denmark)
Laugesen, Anders Rosenstand
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...
Population Monotonic Path Schemes for Simple Games
Ciftci, B.B.; Borm, P.E.M.; Hamers, H.J.M.
2006-01-01
A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path.A path scheme is called population monotonic if a player's payoff does not decrease as the pa
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES
Institute of Scientific and Technical Information of China (English)
XU XIAOQUAN; LIU YINGMING
2004-01-01
In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the UrysohnNachbin lemma is presented which is quite different from the classical one.
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.
Strong monotonicity for analytic ordinary differential equations
Directory of Open Access Journals (Sweden)
Sebastian Walcher
2009-09-01
Full Text Available We present a necessary and sufficient criterion for the flow of an analytic ordinary differential equation to be strongly monotone; equivalently, strongly order-preserving. The criterion is given in terms of the reducibility set of the derivative of the right-hand side. Some applications to systems relevant in biology and ecology, including nonlinear compartmental systems, are discussed.
Limit properties of monotone matrix functions
Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk; Wietsma, Rudi
2012-01-01
The basic objects in this paper are monotonically nondecreasing n x n matrix functions D(center dot) defined on some open interval l = (a, b) of R and their limit values D(a) and D(b) at the endpoints a and b which are, in general, selfadjoint relations in C-n. Certain space decompositions induced b
Concerns on Monotonic Imbalance Bounding Matching Methods
Yatracos, Yannis G.
2013-01-01
Concerns are expressed for the Monotonic Imbalance Bounding (MIB) property (Iacus et al. 2011) and for MIB matching because i) the definition of the MIB property leads to inconsistencies and the nature of the imbalance measure is not clearly defined, ii) MIB property does not generalize Equal Percent Bias Reducing (EPBR) property, iii) MIB matching does not provide statistical information available with EPBR matching.
Nonparametric confidence intervals for monotone functions
Groeneboom, P.; Jongbloed, G.
2015-01-01
We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699–1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the trea
Nonparametric confidence intervals for monotone functions
Groeneboom, P.; Jongbloed, G.
2015-01-01
We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699–1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the
Edit Distance to Monotonicity in Sliding Windows
DEFF Research Database (Denmark)
Chan, Ho-Leung; Lam, Tak-Wah; Lee, Lap Kei
2011-01-01
of a data stream is becoming well-understood over the past few years. Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the w most recent items in the stream for any w ≥ 1. We give a deterministic...
Tracking algorithms for multiagent systems.
Meng, Deyuan; Jia, Yingmin; Du, Junping; Yu, Fashan
2013-10-01
This paper is devoted to the consensus tracking issue on multiagent systems. Instead of enabling the networked agents to reach an agreement asymptotically as the time tends to infinity, the consensus tracking between agents is considered to be derived on a finite time interval as accurately as possible. We thus propose a learning algorithm with a gain operator to be determined. If the gain operator is designed in the form of a polynomial expression, a necessary and sufficient condition is obtained for the networked agents to accomplish the consensus tracking objective, regardless of the relative degree of the system model of agents. Moreover, the H∞ analysis approach is introduced to help establish conditions in terms of linear matrix inequalities (LMIs) such that the resulting processes of the presented learning algorithm can be guaranteed to monotonically converge in an iterative manner. The established LMI conditions can also enable the iterative learning processes to converge with an exponentially fast speed. In addition, we extend the learning algorithm to address the relative formation problem for multiagent systems. Numerical simulations are performed to demonstrate the effectiveness of learning algorithms in achieving both consensus tracking and relative formation objectives for the networked agents.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A noninterior continuation method is proposed for semidefinite complementarity problem (SDCP). This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are: (i)it is well defined for the monotones SDCP; (ii) it has to solve just one linear system of equations at each step; (iii) it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.
Institute of Scientific and Technical Information of China (English)
Gang CAI; Shangquan BU
2013-01-01
In this paper,we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces.Then we study the weak convergence of the two iterative sequences.Our results improve and extend the results announced by many others.
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.
Quantum Algorithms with Fixed Points: The Case of Database Search
Grover, L K; Tulsi, T; Grover, Lov K.; Patel, Apoorva; Tulsi, Tathagat
2006-01-01
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\\frac{\\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\\epsilon$ to $\\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.
Computation of non-monotonic Lyapunov functions for continuous-time systems
Li, Huijuan; Liu, AnPing
2017-09-01
In this paper, we propose two methods to compute non-monotonic Lyapunov functions for continuous-time systems which are asymptotically stable. The first method is to solve a linear optimization problem on a compact and bounded set. The proposed linear programming based algorithm delivers a CPA1
Rates of Convergence of Recursively Defined Sequences
DEFF Research Database (Denmark)
Lambov, Branimir Zdravkov
2005-01-01
This paper gives a generalization of a result by Matiyasevich which gives explicit rates of convergence for monotone recursively defined sequences. The generalization is motivated by recent developments in fixed point theory and the search for applications of proof mining to the field. It relaxes...... the requirement for monotonicity to the form xn+1 ≤ (1+an)xn+bn where the parameter sequences have to be bounded in sum, and also provides means to treat computational errors. The paper also gives an example result, an application of proof mining to fixed point theory, that can be achieved by the means discussed...
Monotone operators and "bigger conjugate" functions
Bauschke, Heinz H; Wang, Xianfu; Yao, Liangjin
2011-01-01
We study a question posed by Stephen Simons in his 2008 monograph involving "bigger conjugate" (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools for further analysis of BC--functions which allow us to answer Simons' problem in the negative. We are also able to refute a similar but much harder conjecture which would have generalized a classical result of Br\\'ezis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.
Convex functions, monotone operators and differentiability
Phelps, Robert R
1993-01-01
The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational princ...
Complexity of Non-Monotonic Logics
Thomas, Michael
2010-01-01
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been considered, e.g., extension with default rules, extension with modal belief operators, or modification of the semantics. In this survey we consider a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription. Additionally, we consider abduction, where one is not interested in inferences from a given knowledge base but in computing possible explanations for an observation with respect to a given knowledge base. Complexity results for different reasoning tasks for propositional variants of these logics have been studied already in the nineties. In recent years, however, a renewed interest in complexity issues can be observed. One current focal approach is to consider parameterized problems and ...
Linear Inviscid Damping for Monotone Shear Flows
Zillinger, Christian
2014-01-01
In this article we prove linear stability, inviscid damping and scattering of the 2D Euler equations around regular, strictly monotone shear flows $(U(y),0)$ in a periodic channel under Sobolev perturbations. We treat the settings of an infinite channel, $\\mathbb{T} \\times \\mathbb{R}$, as well as a finite channel, $\\mathbb{T} \\times [0,1]$, with impermeable boundary. We first prove inviscid damping with optimal algebraic rates for strictly monotone shear flows under the assumption of controlling the regularity of the scattered vorticity. Subsequently, we establish linear stability of the scattering equation in Sobolev spaces under perturbations which are of not too large wave-length with respect to $x$, depending on $U''$.
Institute of Scientific and Technical Information of China (English)
李鹏; 郑志强
2011-01-01
基于非光滑的类二次型Lyapunov函数，对二阶滑模Supevtwisfing算法的有限时间收敛性进行了分析．当系统受常值干扰时，通过Lyapunov方程证明了该算法有限时间收敛，并给出了收敛时间的最优估计；当系统受时变干扰时，通过求解代数Riccati方程得出了一组保证该算法有限时间收敛的参数取值范围，并给出了收敛时间的估计值．仿真算例表明了理论分析的正确性．%The finite time convergence of the second order sliding Super-twisting algorithm is analyzed by using a non- smooth quadratic-like Lyapunov function. For the constant disturbance, the finite time convergence is proved through Lyapunov equation, and the optimal estimation of the convergence time is presented. For the time varying disturbance, the finite time convergence of Super-twisting is guaranteed when the parameters satisfy the algebraic Riccati equation, and the estimation of the convergence time is provided. Finally, simulation results show the correction of the theoretical analysis.
Weak Convergence and Weak Convergence
Directory of Open Access Journals (Sweden)
Narita Keiko
2015-09-01
Full Text Available In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By RNS_Real Mizar functor, real normed spaces as real number spaces already defined in the article [18], we regarded sequences of real numbers as sequences of RNS_Real. So we proved the last theorem in this section using the theorem (8 from [25]. In Section 3, we defined weak sequential compactness of real normed spaces. We showed some lemmas for the proof and proved the theorem of weak sequential compactness of reflexive real Banach spaces. We referred to [36], [23], [24] and [3] in the formalization.
Institute of Scientific and Technical Information of China (English)
颜丽蓉; 郭里婷
2013-01-01
针对基于LUT的自适应预失真技术查询表收敛速度慢的缺陷,从以下两个方面进行改进:采用变步长的RASCAL算法；在查询表收敛过程中,对其进行拉格朗日内插.基于Matlab,从算法收敛曲线、星座图、功率谱以及误比特率几个方面对算法的性能进行仿真比较,仿真结果及分析表明所改进算法的优越性.%Referring to the weakness of slow convergent speed of adaptive predistortion based on LUT, efforts are made through two aspects: one is to make use of variable - step RASCAL algorithm, the other is to use Lagrange interpolation in the progress of LUT' s convergence. Through Matlab simulation. the performance of adaptive algorithm is compared and analyzed in terms of algorithm' s convergent curve, constellation, PSD and bit error rate. Simulation results and analysis demonstrate the better performance of the proposed method.
Is the convergence of the manufacturing sector unconditional?
Directory of Open Access Journals (Sweden)
Juliano Assunção
2015-09-01
Full Text Available In Unconditional Convergence, Rodrik (2011b documented that manufacturing industries exhibit unconditional convergence in labor productivity. We provide a novel semi-parametric specification for convergence equations and show that the speed of convergence varies systematically with country-specific characteristics. We consider the flexible smooth transition model with multiple transition variables, which allows each group to have distinct dynamics controlled by a linear combination of known variables. We found evidence that the laws of motion for industry productivity growth are different across countries, varying with political institutions. The speed of convergence also has a non-monotonic relationship with trade openness and education.
Weak monotonicity inequality and partial regularity for harmonic maps
Institute of Scientific and Technical Information of China (English)
沈尧天; 严树森
1999-01-01
The notion of locally weak monotonicity inequality for weakly harmonic maps is introduced and various results on this class of maps are obtained. For example, the locally weak monotonicity inequality is nearly equivalent to the ε-regularity.
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 beha...
MINLIP for the Identification of Monotone Wiener Systems
Pelckmans, Kristiaan
2010-01-01
This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques.
A-monotonicity and applications to nonlinear variational inclusion problems
Directory of Open Access Journals (Sweden)
Ram U. Verma
2004-01-01
Full Text Available A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity. Since the A-monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.
On the strong monotonicity of the CABARET scheme
Ostapenko, V. V.
2012-03-01
The strong monotonicity of the CABARET scheme with single flux correction is analyzed as applied to the linear advection equation. It is shown that the scheme is strongly monotone (has the NED property) at Courant numbers r ∈ (0,0,5), for which it is monotone. Test computations illustrating this property of the CABARET scheme are presented.
Testing Manifest Monotonicity Using Order-Constrained Statistical Inference
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,…
PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS
Institute of Scientific and Technical Information of China (English)
DING Xie-ping; LIN Yen-cherng; YAO Jen-chih
2006-01-01
A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings.
A New Nonmonotonic Trust Region Algorithm for A Class of Unconstraied Nonsmooth Optimization
Institute of Scientific and Technical Information of China (English)
欧宜贵; 侯定丕
2002-01-01
This paper preasents a new trust region algorithm for solving a class of composite nonsmooth optimizations.It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive itereates and that this method extends the existing results for this type of nonlinear optimization with smooth ,or piecewis somooth,or convex objective functions or their composition It is pyoved that this algorithm is globally convergent under certain conditions.Finally,some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.
Wehrl entropy, Lieb conjecture and entanglement monotones
Mintert, F; Mintert, Florian; Zyczkowski, Karol
2004-01-01
We propose to quantify the entanglement of pure states of $N \\times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure state analyzed is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (R{\\'e}nyi) subentropies, are proved to be Schur--convex, so they are entanglement monotones and may be used as alternative measures of entanglement.
Generalized monotone method and numerical approach for coupled reaction diffusion systems
Sowmya, M.; Vatsala, Aghalaya S.
2017-01-01
Study of coupled reaction diffusion systems are very useful in various branches of science and engineering. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, with initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to the unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical methodology.
Topological recursion and a quantum curve for monotone Hurwitz numbers
Do, Norman; Dyer, Alastair; Mathews, Daniel V.
2017-10-01
Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. Monotone Hurwitz numbers restrict the enumeration by imposing a further monotonicity condition on such factorisations. In this paper, we prove that monotone Hurwitz numbers arise from the topological recursion of Eynard and Orantin applied to a particular spectral curve. We furthermore derive a quantum curve for monotone Hurwitz numbers. These results extend the collection of enumerative problems known to be governed by the paradigm of topological recursion and quantum curves, as well as the list of analogues between monotone Hurwitz numbers and their classical counterparts.
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.
Variable selection in monotone single-index models via the adaptive LASSO.
Foster, Jared C; Taylor, Jeremy M G; Nan, Bin
2013-09-30
We consider the problem of variable selection for monotone single-index models. A single-index model assumes that the expectation of the outcome is an unknown function of a linear combination of covariates. Assuming monotonicity of the unknown function is often reasonable and allows for more straightforward inference. We present an adaptive LASSO penalized least squares approach to estimating the index parameter and the unknown function in these models for continuous outcome. Monotone function estimates are achieved using the pooled adjacent violators algorithm, followed by kernel regression. In the iterative estimation process, a linear approximation to the unknown function is used, therefore reducing the situation to that of linear regression and allowing for the use of standard LASSO algorithms, such as coordinate descent. Results of a simulation study indicate that the proposed methods perform well under a variety of circumstances and that an assumption of monotonicity, when appropriate, noticeably improves performance. The proposed methods are applied to data from a randomized clinical trial for the treatment of a critical illness in the intensive care unit.
Completely Monotone Multisequences, Symmetric Probabilities and a Normal Limit Theorem
Indian Academy of Sciences (India)
J C Gupta
2000-11-01
Let G, be the set of all partial completely monotone multisequences of order and degree , i.e., multisequences (1, 2,$\\ldots$ ,k), 1, 2,$\\ldots$ , = 0, 1, 2,$\\ldots$ ,1 + 2 + \\$cdots$ + ≤ n, (0,0,$\\ldots$ ,0) = 1 and $(-1)^{_0}^{_0}$ (1, 2,$\\ldots$ ,)≥ 0 whenever 0 ≤ -(1 + 2 +$\\cdots$ +) where (1, 2,$\\ldots$ ,)=(1+1, 2,$\\ldots$ ,)+ (1,2+1,$\\ldots$ ,)+$\\cdots$ + (1, 2,$\\ldots$ ,+1)-(1,2,$\\ldots$ ,)$. Further, let $\\prod_{n,k}$ be the set of all symmetric probabilities on ${0, 1, 2,\\ldots ,k}^{n}$. We establish a one-to-one correspondence between the sets G, and $\\prod_{n, k}$ and use it to formulate and answer interesting questions about both. Assigning to G, the uniform probability measure, we show that, as → ∞ , any fixed section {(1, 2,$\\ldots$ ,), 1 ≤ $\\sum ≤ }, properly centered and normalized, is asymptotically multivariate normal. That is, $\\left\\{\\sqrt{\\left(\\binom{n+k}{k}\\right)}((1, 2,\\ldots ,)-c_0(1, 2,\\ldots ,), 1≤ _1+2+\\cdots +_k≤ m\\right\\}$ converges weakly to MVN[0,]; the centering constants 0(1, 2,$\\ldots$ ,) and the asymptotic covariances depend on the moments of the Dirichlet $(1, 1,\\ldots ,1; 1)$ distribution on the standard simplex in .
Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael
2017-07-01
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.
Payoff-monotonic game dynamics and the maximum clique problem.
Pelillo, Marcello; Torsello, Andrea
2006-05-01
Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties of these models, which, under a certain symmetry assumption, possess a Lyapunov function. In this letter, we generalize previous work along these lines in several respects. We introduce a wide family of game-dynamic equations known as payoff-monotonic dynamics, of which replicator dynamics are a special instance, and show that they enjoy precisely the same dynamical properties as standard replicator equations. These properties make any member of this family a potential heuristic for solving standard quadratic programs and, in particular, the maximum clique problem. Extensive simulations, performed on random as well as DIMACS benchmark graphs, show that this class contains dynamics that are considerably faster than and at least as accurate as replicator equations. One problem associated with these models, however, relates to their inability to escape from poor local solutions. To overcome this drawback, we focus on a particular subclass of payoff-monotonic dynamics used to model the evolution of behavior via imitation processes and study the stability of their equilibria when a regularization parameter is allowed to take on negative values. A detailed analysis of these properties suggests a whole class of annealed imitation heuristics for the maximum clique problem, which are based on the idea of varying the parameter during the imitation optimization process in a principled way, so as to avoid unwanted inefficient solutions. Experiments show that the proposed annealing procedure does help to avoid poor local optima by initially driving the dynamics toward promising regions in
Max-Sum Diversification, Monotone Submodular Functions and Dynamic Updates
Borodin, Allan; Ye, Yuli
2012-01-01
Result diversification has many important applications in databases, operations research, information retrieval, and finance. In this paper, we study and extend a particular version of result diversification, known as max-sum diversification. More specifically, we consider the setting where we are given a set of elements in a metric space and a set valuation function $f$ defined on every subset. For any given subset $S$, the overall objective is a linear combination of $f(S)$ and the sum of the distances induced by $S$. The goal is to find a subset $S$ satisfying some constraints that maximizes the overall objective. This problem is first studied by Gollapudi and Sharma for modular set functions and for sets satisfying a cardinality constraint. We consider an extension of the modular case to the monotone submodular case, for which the previous algorithm no longer applies. Interestingly, we are able to match the 2-approximation using a natural, but different greedy algorithm. We then further extend the problem...
Convex functions, monotone operators and differentiability
Phelps, Robert R
1989-01-01
These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.
Generalized convexity, generalized monotonicity recent results
Martinez-Legaz, Juan-Enrique; Volle, Michel
1998-01-01
A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized conve...
Ioan Boţ, Radu; Hofmann, Bernd
2016-12-01
In the literature on singular perturbation (Lavrentiev regularization) for the stable approximate solution of operator equations with monotone operators in the Hilbert space the phenomena of conditional stability and local well-posedness or ill-posedness are rarely investigated. Our goal is to present some studies which try to bridge this gap. So we present new results on the impact of conditional stability on error estimates and convergence rates for the Lavrentiev regularization and distinguish for linear problems well-posedness and ill-posedness in a specific manner motivated by a saturation result. Taking into account that the behavior of the bias (regularization error in the noise-free case) is crucial, general convergence rates, including logarithmic rates, are derived for linear operator equations by means of the method of approximate source conditions. This allows us to extend well-known convergence rate results for the Lavrentiev regularization that were based on general source conditions to the case of non-selfadjoint linear monotone forward operators for which general source conditions fail. Examples presenting the self-adjoint multiplication operator as well as the non-selfadjoint fractional integral operator and Cesàro operator illustrate the theoretical results. Extensions to the nonlinear case under specific conditions on the nonlinearity structure complete the paper.
Problèmes de convergence d'algorithmes dans la détermination de trajectoires perturbées.
Bec-Borsenberger, A.; Bougeard, M. L.
The problem of the robustness of the algorithms used is studied in the case of the determination of trajectories of objects submitted to perturbations. The algorithm used is presented here and the numerical resolution is given; the notions of stability and robustness are distinguished and a procedure to obtain a robust solution is detailed.
Institute of Scientific and Technical Information of China (English)
曹丽霞
2012-01-01
In this paper, using the Fischer function , the generalized horizontal linear complementarity problem （HLCP）is reformulated as a system of nonsmooth equations. With the Levenberg - Marquardt algorithm, a new approach is employed for obtaining its solution. At the same time, the L- M algorithm is both globally and quadratically convergent without nondegenerate solution.%借助Fischer函数将广义水平线性互补问题（HLCP）等价转化为一个方程系统，并利用Levenberg-Marquardt方法，给出一种求解船的新方法，同时在不要求存在非退化解的条件下证明了这种方法的全局和二次收敛。
An improved proximal-based decomposition method for structured monotone variational inequalities
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The proximal-based decomposition method was originally proposed by Chen and Teboulle (Math. Programming, 1994, 64:81-101 for solving convex minimization problems. This paper extends it to solving monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem's data as the original method.
Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions
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...
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
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.
On the monotonicity of multidimensional finite difference schemes
Kovyrkina, O.; Ostapenko, V.
2016-10-01
The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.
Institute of Scientific and Technical Information of China (English)
朱冰莲; 运明华; 钱明达; 张磊
2012-01-01
针对认知无线电中分布式功率控制算法收敛速度较慢的问题,提出了一种新的非合作博弈模型下的功率控制算法.算法主要通过构造基于信干比(SIR)的正切型代价函数来减少迭代次数,从而提高收敛速度.仿真结果表明,所提算法在满足认知用户信干比要求和主用户干扰温度容限下,与Koskie-Gajic算法和自适应功率控制(CRNCPCG)算法相比,在收敛速度上有了大幅度的提高,能更好地满足系统实时性要求,并且在用户数小于20时,平均信干比至少提高了0.3 dB,可以实现对认知用户发射功率的有效控制.%Concerning the slow convergence of distributed power control algorithm in cognitive radio, a novel algorithm based on non-cooperative game was proposed for cognitive radio system. A Signal-to-Interference Ratio (SIR) -based tangent cost function of fewer iterations was designed to improve the convergence. The simulation results demonstrate that, compared with the Koskie-Gajic algorithm and the Cognitive Radios-Non-Cooperative Power Control Game (CR-NCPCG) algorithm, the proposed algorithm at the premise of satisfying the secondary users' demand for SIR and the primary user's interference temperature constraint, not only can fast converge, but also has higher average SIR with at least 0.3 dB when the number of users is less than twenty. It can control the power of secondary users effectively.
Probabilistic Analysis of Pattern Formation in Monotonic Self-Assembly.
Moore, Tyler G; Garzon, Max H; Deaton, Russell J
2015-01-01
Inspired by biological systems, self-assembly aims to construct complex structures. It functions through piece-wise, local interactions among component parts and has the potential to produce novel materials and devices at the nanoscale. Algorithmic self-assembly models the product of self-assembly as the output of some computational process, and attempts to control the process of assembly algorithmically. Though providing fundamental insights, these computational models have yet to fully account for the randomness that is inherent in experimental realizations, which tend to be based on trial and error methods. In order to develop a method of analysis that addresses experimental parameters, such as error and yield, this work focuses on the capability of assembly systems to produce a pre-determined set of target patterns, either accurately or perhaps only approximately. Self-assembly systems that assemble patterns that are similar to the targets in a significant percentage are "strong" assemblers. In addition, assemblers should predominantly produce target patterns, with a small percentage of errors or junk. These definitions approximate notions of yield and purity in chemistry and manufacturing. By combining these definitions, a criterion for efficient assembly is developed that can be used to compare the ability of different assembly systems to produce a given target set. Efficiency is a composite measure of the accuracy and purity of an assembler. Typical examples in algorithmic assembly are assessed in the context of these metrics. In addition to validating the method, they also provide some insight that might be used to guide experimentation. Finally, some general results are established that, for efficient assembly, imply that every target pattern is guaranteed to be assembled with a minimum common positive probability, regardless of its size, and that a trichotomy exists to characterize the global behavior of typical efficient, monotonic self-assembly systems
Probabilistic Analysis of Pattern Formation in Monotonic Self-Assembly.
Directory of Open Access Journals (Sweden)
Tyler G Moore
Full Text Available Inspired by biological systems, self-assembly aims to construct complex structures. It functions through piece-wise, local interactions among component parts and has the potential to produce novel materials and devices at the nanoscale. Algorithmic self-assembly models the product of self-assembly as the output of some computational process, and attempts to control the process of assembly algorithmically. Though providing fundamental insights, these computational models have yet to fully account for the randomness that is inherent in experimental realizations, which tend to be based on trial and error methods. In order to develop a method of analysis that addresses experimental parameters, such as error and yield, this work focuses on the capability of assembly systems to produce a pre-determined set of target patterns, either accurately or perhaps only approximately. Self-assembly systems that assemble patterns that are similar to the targets in a significant percentage are "strong" assemblers. In addition, assemblers should predominantly produce target patterns, with a small percentage of errors or junk. These definitions approximate notions of yield and purity in chemistry and manufacturing. By combining these definitions, a criterion for efficient assembly is developed that can be used to compare the ability of different assembly systems to produce a given target set. Efficiency is a composite measure of the accuracy and purity of an assembler. Typical examples in algorithmic assembly are assessed in the context of these metrics. In addition to validating the method, they also provide some insight that might be used to guide experimentation. Finally, some general results are established that, for efficient assembly, imply that every target pattern is guaranteed to be assembled with a minimum common positive probability, regardless of its size, and that a trichotomy exists to characterize the global behavior of typical efficient, monotonic
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.
Institute of Scientific and Technical Information of China (English)
邵言剑; 陶卿; 姜纪远; 周柏
2014-01-01
Stochastic gradient descent (SGD) is one of the efficient methods for dealing with large-scale data. Recent research shows that the black-box SGD method can reach an O(1/T) convergence rate for strongly-convex problems. However, for solving the regularized problem with L1 plus L2 terms, the convergence rate of the structural optimization method such as COMID (composite objective mirror descent) can only attain O(lnT/T). In this paper, a weighted algorithm based on COMID is presented, to keep the sparsity imposed by the L1 regularization term. A prove is provided to show that it achieves an O(1/T) convergence rate. Furthermore, the proposed scheme takes the advantage of computation on-the-fly so that the computational costs are reduced. The experimental results demonstrate the correctness of theoretic analysis and effectiveness of the proposed algorithm.%随机梯度下降(SGD)算法是处理大规模数据的有效方法之一。黑箱方法SGD在强凸条件下能达到最优的O(1/T)收敛速率，但对于求解L1+L2正则化学习问题的结构优化算法，如COMID(composite objective mirror descent)仅具有O(lnT/T)的收敛速率。提出一种能够保证稀疏性基于COMID的加权算法，证明了其不仅具有O(1/T)的收敛速率，还具有on-the-fly计算的优点，从而减少了计算代价。实验结果表明了理论分析的正确性和所提算法的有效性。
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Remarks on a monotone Markov chain
Directory of Open Access Journals (Sweden)
P. Todorovic
1987-01-01
Full Text Available In applications, considerations on stochastic models often involve a Markov chain {ζn}0∞ with state space in R+, and a transition probability Q. For each x R+ the support of Q(x,. is [0,x]. This implies that ζ0≥ζ1≥…. Under certain regularity assumptions on Q we show that Qn(x,Bu→1 as n→∞ for all u>0 and that 1−Qn(x,Bu≤[1−Q(x,Bu]n where Bu=[0,u. Set τ0=max{k;ζk=ζ0}, τn=max{k;ζk=ζτn−1+1} and write Xn=ζτn−1+1, Tn=τn−τn−1. We investigate some properties of the imbedded Markov chain {Xn}0∞ and of {Tn}0∞. We determine all the marginal distributions of {Tn}0∞ and show that it is asymptotically stationary and that it possesses a monotonicity property. We also prove that under some mild regularity assumptions on β(x=1−Q(x,Bx, ∑1n(Ti−a/bn→dZ∼N(0,1.
Strong convergence theorems for strongly relatively nonexpansive sequences and applications
Aoyama, Koji; Kohsaka, Fumiaki
2012-01-01
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem for a maximal monotone operator and the fixed point problem for a relatively nonexpansive mapping.
A New Look at the Convergence of a Famous Sequence
Dobrescu, Mihaela
2010-01-01
A new proof for the monotonicity of the sequence [image omitted] is given as a special case of a large family of monotomic and bounded, hence convergent sequences. The new proof is based on basic calculus results rather than induction, which makes it accessible to a larger audience including business and life sciences students and faculty. The…
Directory of Open Access Journals (Sweden)
Yeol Je Cho
2008-03-01
Full Text Available Two iterative schemes for finding a common element of the set of zero points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are obtained. Two strong convergence theorems are obtained which extend some previous work. Moreover, the applications of the iterative schemes are demonstrated.
Directory of Open Access Journals (Sweden)
Cho YeolJe
2007-01-01
Full Text Available Two iterative schemes for finding a common element of the set of zero points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are obtained. Two strong convergence theorems are obtained which extend some previous work. Moreover, the applications of the iterative schemes are demonstrated.
Surface meshing with curvature convergence
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.
基于三次B样条的曲线逼近算法及其收敛性%Approximate algorithm of curves and its convergence based on cubic B-spline
Institute of Scientific and Technical Information of China (English)
蒋勇; 李玉梅
2013-01-01
为了改进传统的插值样条曲线算法不易于后期处理和实时局部修改、B样条算法不能满足精度要求的缺点,提出了一种基于三次B样条的曲线逼近算法[1].该算法以三次B样条为基础对曲线的逼近领域进行了研究,通过大量的数值实验证明了该算法的可行性及高效性.该算法通过结合插值样条与B样条的各种优点,有效避免了传统算法的不足.同时,对该算法的收敛性进行了理论证明.数值实验表明了该算法具有收敛速度快、精度高且编程易实现等优点,为曲线研究提供了可供参考的有效算法.%In order to improve the shortcomings of the traditional interpolation spline that is not easy to solve the problems at the post-processing and to do the local modification in time,and to improve the disadvantage of the approximate spline which can not meet the accuracy requirements,the approximate algorithm based on the cubic B-Spline is put forward[1].The algorithm is based on the cubic B-Spline and makes some research on the area of the curve approximate.A large number of numerical experiments are made to illustrate the feasibility and the efficiency of the algorithm.The algrithm combines the advantages of the interpolation spline and the B-Spline.The shortcomings of the traditional algrithrn are prevented effectively.At the same time,the theoretical proof is put forward to demonstrate the convergence of the algorithm.And the numerical experiments show that this algorithm has fast convergence speed and high precision.And its programming is easy to implement.A effective algorithm is put forward for the curve research which can be use as a reference.
Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface
Directory of Open Access Journals (Sweden)
Xinru Liu
2014-01-01
Full Text Available A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.
Monotone complete C*-algebras and generic dynamics
Saitô, Kazuyuki
2015-01-01
This monograph is about monotone complete C*-algebras, their properties and the new classification theory. A self-contained introduction to generic dynamics is also included because of its important connections to these algebras. Our knowledge and understanding of monotone complete C*-algebras has been transformed in recent years. This is a very exciting stage in their development, with much discovered but with many mysteries to unravel. This book is intended to encourage graduate students and working mathematicians to attack some of these difficult questions. Each bounded, upward directed net of real numbers has a limit. Monotone complete algebras of operators have a similar property. In particular, every von Neumann algebra is monotone complete but the converse is false. Written by major contributors to this field, Monotone Complete C*-algebras and Generic Dynamics takes readers from the basics to recent advances. The prerequisites are a grounding in functional analysis, some point set topology and an eleme...
A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone
Directory of Open Access Journals (Sweden)
Zhang Ying
2011-01-01
Full Text Available Abstract In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equations, and a smoothing-type method is proposed to solve it iteratively so that a solution of the system of inequalities is found. By means of the theory of Euclidean Jordan algebras, the algorithm is proved to be well defined, and to be globally convergent under weak assumptions and locally quadratically convergent under suitable assumptions. Preliminary numerical results indicate that the algorithm is effective. AMS subject classifications: 90C33, 65K10.
Institute of Scientific and Technical Information of China (English)
谢承旺
2012-01-01
There exsits a performance crisis for modern multi-objective evolutionary algorithms in high-dimensional objective space.In this paper,a hybird many-objective evolutionary algorithm（HMOEA） is proposed to improve MOEA＇s performance in solving many-objective optimization problems.In the HMOEA,w-dominance relation based on revaluation function is used to replace the Pareto-dominance relation,secondly,to balance the convergence and diversity in evolutionary population,the composition of the next population is varying with the current generation.Finally,an improved crowding distance assignment is used in HMOEA to evaluate individual＇s density to preserve diversity.HMOEA is examined on DTLZ2 to observe its performance in many-objective optimization problems.Experimental results illustrate that HMOEA exhibits a good performance in sense of convergence and diversity.At last,it is proven that the new algorithm can guarantee the convergence towards the global optimum under some conditions.%现代多目标进化算法在高维目标空间中遭遇性能危机,提出一种混合高维目标进化算法（Hybrid Many-Ob-jective Evolutionary Algorithm,HMOEA）以改善算法的解题性能.新的算法使用了新定义的w-支配关系替代Pa-reto支配关系;其次,为使算法在收敛性与多样性之间保持适当均衡,下一代种群个体的构成随当前进化世代动态调整;最后,算法使用了改进的拥挤距离赋值机制评估解个体密度以实施多样性保持操作.新算法在DTLZ2问题上进行测试,结果表明该算法可以获得很好的性能,而且新算法在收敛性和多样性之间也取得了较好的均衡.最后,从一般意义上分析了HMOEA算法的收敛性,分析结果表明HMOEA算法能够以概率1收敛.
Institute of Scientific and Technical Information of China (English)
胡浩; 李刚
2015-01-01
Though evolutionary algorithms (EAs)are capable of satisfying the demands arising from the new advancements in structural topology optimization on global optimization,black-box function optimi-zation,combinatorial optimization and multi-objective optimization,the necessity of applying them to this field still depends on their convergence and computational efficiency simultaneously.This paper aims to reveal competent algorithms on these two aspects for stress constrained truss multi-objective topology optimization (MOTO)problems.We first propose a general method tailor-made for examining the convergence and efficiency of EAs on solving MOTO.The global optima of typical MOTO problems are rigorously derived using enumeration.Then multi-level convergence criteria are defined using hypervol-ume metric.The comparative study reveals outstanding EAs with greatest convergence speeds under different convergence requirement and the corresponding algorithmic mechanism.This way,this paper not only contributes to the theoretical foundation of solving MOTO problems using EAs,but also provides support for high efficiently solving practical engineering topology optimization problems.%演化算法能够同时满足结构拓扑优化的前沿领域对全局优化、黑箱函数优化、组合优化和多目标优化的需求，但采用此类算法的可行性与必要性由其收敛性与计算效率决定。本文以应力约束桁架多目标拓扑优化问题为求解对象，致力于揭示在收敛性与计算效率两方面具有竞争力的算法。首先提出评估演化算法求解拓扑优化问题收敛性与计算效率的通用方法，采用穷举法严格推导了典型桁架多目标拓扑优化问题的全局最优解，并采用超体积指标定义了多层次收敛性能准则。最后通过比较研究得到不同收敛性需求下具有最快收敛速度的演化算法，并揭示了具有竞争力的算法机制。本研究为演化算法求解多目标拓
The Number of Monotone and Self-Dual Boolean Functions
Directory of Open Access Journals (Sweden)
Haviarova L.
2014-12-01
Full Text Available In the present paper we study properties of pre-complete class of Boolean functions - monotone Boolean functions. We discuss interval graph, the abbreviated d.n.f., a minimal d.n.f. and a shortest d.n.f. of this function. Then we present a d.n.f. with the highest number of conjunctionsand we determinate the exact number of them. We count the number of monotone Boolean functions with some special properties. In the end we estimate the number of Boolean functionthat are monotone and self-dual at the same time.
Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences
Chen, William Y C; Zhou, Elaine L F
2010-01-01
The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x+1), which leads to the log-concavity of P(x+c) for any $c\\geq 1$ due to Llamas and Mart\\'{\\i}nez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Chen and Xia without resorting to the recurrence relations of the coefficients.
Self-Adaptive Implicit Methods for Monotone Variant Variational Inequalities
Directory of Open Access Journals (Sweden)
Ge Zhili
2009-01-01
Full Text Available The efficiency of the implicit method proposed by He (1999 depends on the parameter heavily; while it varies for individual problem, that is, different problem has different "suitable" parameter, which is difficult to find. In this paper, we present a modified implicit method, which adjusts the parameter automatically per iteration, based on the message from former iterates. To improve the performance of the algorithm, an inexact version is proposed, where the subproblem is just solved approximately. Under mild conditions as those for variational inequalities, we prove the global convergence of both exact and inexact versions of the new method. We also present several preliminary numerical results, which demonstrate that the self-adaptive implicit method, especially the inexact version, is efficient and robust.
Institute of Scientific and Technical Information of China (English)
周柏; 陶卿; 储德军
2015-01-01
几乎所有的稀疏随机算法都来源于在线形式，只能获得平均输出方式的收敛速率，对于强凸优化问题无法达到最优的瞬时收敛速率.文中避开在线形式转到随机模式，直接研究随机优化算法.首先在含有 L1正则化项的稀疏优化问题中加入 L2正则化项，使之具有强凸特性.然后将黑箱优化方法中的随机步长策略引入到当前通用的结构优化算法 COMID 中，得到基于随机步长的混合正则化镜面下降稀疏随机优化算法.最后通过分析 L1正则化问题中软阈值方法的求解特点，证明算法具有最优的瞬时收敛速率.实验表明，文中算法的稀疏性优于 COMID.%Almost all sparse stochastic algorithms are developed from the online setting, and only the convergence rate of average output can be obtained. The optimal rate for strongly convex optimization problems can not be reached as well. The stochastic optimization algorithms are directly studied instead of the online to batch conversation in this paper. Firstly, by incorporating the L2 regularizer into the L1-regularized sparse optimization problems, the strong convexity can be obtained. Then, by introducing the random step-size strategy from the black-box optimization method to the state-of-the-art algorithm-composite objective mirror descent (COMID), a sparse stochastic optimization algorithm based introducing on random step-size hybrid regularized mirror descent ( RS-HMD) is achieved. Finally, based on the analysis of characteristics of soft threshold methods in solving the L1-regularized problem, the optimal individual convergence rate is proved. Experimental results demonstrate that sparsity of RS-HMD is better than that of COMID.
A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC1 OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
ZhangLiping; LaiYanlian
2001-01-01
Abstract. A new trust region algorithm for solving convex LC1 optimization problem is present-ed. It is proved that the algorithm is globally convergent and the rate of convergence is superlin-ear under some reasonable assumptions.
On the Monotone Iterative Method for Set Valued Equation
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper deals with the monotone iterative method for set- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.
Monotone method for initial value problem for fractional diffusion equation
Institute of Scientific and Technical Information of China (English)
ZHANG Shuqin
2006-01-01
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
Action-Maslov Homomorphism for Monotone Symplectic Manifolds
Branson, Mark
2009-01-01
We explore conditions under which the action-Maslov homomorphism vanishes on monotone symplectic manifolds. Our strategy involves showing that the units in the quantum homology, and thus the Seidel element, have a very specific form. Then we use induction to show that other relevant Gromov-Witten invariants vanish. We prove that these conditions hold for monotone products of projective spaces and for the Grassmannian of 2-planes in $\\C^4$.
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....
Isotonicity of the projection onto the monotone cone
Németh, A B
2012-01-01
A wedge (i.e., a closed nonempty set in the Euclidean space stable under addition and multiplication with non-negative scalars) induces by a standard way a semi-order (a reflexive and transitive binary relation) in the space. The wedges admitting isotone metric projection with respect to the semi-order induced by them are characterized. The obtained result is used to show that the monotone wedge (called monotone cone in regression theory) admits isotone projection.
Monotonic loading of circular surface footings on clay
Energy Technology Data Exchange (ETDEWEB)
Ibsen, Lars Bo; Barari, Amin [Aalborg University, Aalborg (Denmark)
2011-12-15
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.
Layered neural networks with non-monotonic transfer functions
Katayama, Katsuki; Sakata, Yasuo; Horiguchi, Tsuyoshi
2003-01-01
We investigate storage capacity and generalization ability for two types of fully connected layered neural networks with non-monotonic transfer functions; random patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network in which a non-monotonic transfer function of even layers is different from that of odd layers. The other is a layered network with intra-layer connections, in which the non-monotonic transfer function of inter-layer is different from that of intra-layer, and inter-layered neurons and intra-layered neurons are updated alternately. We derive recursion relations for order parameters for those layered networks by the signal-to-noise ratio method. We clarify that the storage capacity and the generalization ability for those layered networks are enhanced in comparison with those with a conventional monotonic transfer function when non-monotonicity of the transfer functions is selected optimally. We also point out that some chaotic behavior appears in the order parameters for the layered networks when non-monotonicity of the transfer functions increases.
Neighborhood-following algorithms for linear programming
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
［1］Kojima, M., Mizuno, S., Yoshise, A., A polynomial-time algorithm for a class of linear complementarity probems, Mathematical Programming, 1989, 44: 1-26.［2］Megiddo, N., Pathways to the optimal set in linear programming. in Progression Mathematical Programming:Interior Point and Related Methods, New York: Springer-Verlag, 1989, 131-158.［3］Monteiro, R. D. C., Adler, I., Interior path following primal-dual algorithms, Part Ⅰ: linear programming, Mathematical Programming, 1989, 44: 27-41.［4］Monteiro, R. D. C., Adler, I., Interior path following primal-dual algorithms, Part Ⅱ: convex quadratic programming, Mathematical Programming, 1989, 44: 43-46.［5］Wright, S. J., Primal-Dual Interior-Point Methods, Philadephia: SIAM Publications, 1997.［6］Mizuno, S., Todd, M. J., Ye, Y., On adaptive step primal-dual interior-point algorithms for linear programming,Mathematics of Operations Research, 1993, 18:964-981.［7］Gonzaga, C. C., The largest step path following algorithm for monotone linear complementarity problems, Mathematical Programming, 1997, 76: 309-332.［8］Sturm, J. F., Zhang, S., On a wide region of centers primal-dual interior point algorithms for linear programming,Tinbergen Institute Rotterdam, Erasmus University, Rotterdam, The Netherlands, 1995.［9］Hung, P., Ye, Y., An asymptotical O(√nL)-iteration path-following linear programming algorithm that uses wide neighborhoods, SIAM J.Optimization, 1996, 6: 570-586.［10］Ye, Y., Interior Point Algorithms: Theory and Analysis, New York: Wiley-Interscience Publication, 1997.［11］Güler, O., Ye, Y., Convergence behavior of interior-point algorithms. Mathematical Programming, 1993, 60:215-228.［12］Mehrotral, S., On the implementation of a primal-dual interior point mehtod, SIAM J. Optimization, 1992, 2(4):575-601.
Auto convergence for stereoscopic 3D cameras
Zhang, Buyue; Kothandaraman, Sreenivas; Batur, Aziz Umit
2012-03-01
Viewing comfort is an important concern for 3-D capable consumer electronics such as 3-D cameras and TVs. Consumer generated content is typically viewed at a close distance which makes the vergence-accommodation conflict particularly pronounced, causing discomfort and eye fatigue. In this paper, we present a Stereo Auto Convergence (SAC) algorithm for consumer 3-D cameras that reduces the vergence-accommodation conflict on the 3-D display by adjusting the depth of the scene automatically. Our algorithm processes stereo video in realtime and shifts each stereo frame horizontally by an appropriate amount to converge on the chosen object in that frame. The algorithm starts by estimating disparities between the left and right image pairs using correlations of the vertical projections of the image data. The estimated disparities are then analyzed by the algorithm to select a point of convergence. The current and target disparities of the chosen convergence point determines how much horizontal shift is needed. A disparity safety check is then performed to determine whether or not the maximum and minimum disparity limits would be exceeded after auto convergence. If the limits would be exceeded, further adjustments are made to satisfy the safety limits. Finally, desired convergence is achieved by shifting the left and the right frames accordingly. Our algorithm runs real-time at 30 fps on a TI OMAP4 processor. It is tested using an OMAP4 embedded prototype stereo 3-D camera. It significantly improves 3-D viewing comfort.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Penalty Algorithms in Hilbert Spaces
Institute of Scientific and Technical Information of China (English)
Jean Pierre DUSSAULT; Hai SHEN; André BANDRAUK
2007-01-01
We analyze the classical penalty algorithm for nonlinear programming in HUbert spaces and obtain global convergence results, as well as asymptotic superlinear convergence order. These convergence results generalize similar results obtained for finite-dimensional problems. Moreover, the nature of the algorithms allows us to solve the unconstrained subproblems in finite-dimensional spaces.
Approximating the Influence of a monotone Boolean function in O(\\sqrt{n}) query complexity
Ron, Dana; Rubinfeld, Ronitt; Safra, Muli; Weinstein, Omri
2011-01-01
The {\\em Total Influence} ({\\em Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function \\ifnum\\plusminus=1 $f: \\{\\pm1\\}^n \\longrightarrow \\{\\pm1\\}$, \\else $f: \\bitset^n \\to \\bitset$, \\fi which we denote by $I[f]$. We present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of $(1\\pm \\eps)$ by performing $O(\\frac{\\sqrt{n}\\log...
Monotone projected gradient methods for large-scale box-constrained quadratic programming
Institute of Scientific and Technical Information of China (English)
ZHOU Bin; GAO Li; DAI Yuhong
2006-01-01
Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
Institute of Scientific and Technical Information of China (English)
王江峰; 伍贻兆; Périaux J
2004-01-01
对比了进化算法(基因算法)与确定性算法(共轭梯度法)在优化控制问题中的优化效率.两种方法都与分散式优化策略-Nash对策进行了结合,并成功地应用于优化控制问题.计算模型采用绕NACA0012翼型的位流流场.区域分裂技术的引用使得全局流场被分裂为多个带有重叠区的子流场,使用4种不同的方法进行当地流场解的耦合,这些算法可以通过当地的流场解求得全局流场解.数值计算结果的对比表明,进化算法可以得到与共轭梯度法相同的计算结果,并且进化算法的不依赖梯度信息的特性使其在复杂问题及非线性问题中具有广泛的应用前景.%The comparison for optimization efficiency between evolutionary algorithms (Genetic Algorithms, GAs) and deterministic algorithms (Conjugate Gradient, CG) is presented. Both two different methods are combined with Nash strategy-decentralized optimization strategy in Game Theory-and implemented into an optimal control problem using a technique DDM (Domain Decomposition Method). The problem consists in simulating the perfect potential flow field around a NACA0012 airfoil with the technique DDM, the global calculation domain is then split into sub-domains with overlaps, the accord of local solutions on interfaces is obtained using four different algorithms which permit the resolution of global problem via local sub-problems on sub-domains and their interfaces. Comparable numerical results are obtained by different algorithms and show that the property of independence of gradient makes GAs based algorithms serious and robust research tools for great dimension problems or non-linear problems.
Driving performance impairments due to hypovigilance on monotonous roads.
Larue, Grégoire S; Rakotonirainy, Andry; Pettitt, Anthony N
2011-11-01
Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Highway design reduces the driving task mainly to a lane-keeping manoeuvre. Such a task is monotonous, providing little stimulation and this contributes to crashes due to inattention. Research has shown that driver's hypovigilance can be assessed with EEG measurements and that driving performance is impaired during prolonged monotonous driving tasks. This paper aims to show that two dimensions of monotony - namely road design and road side variability - decrease vigilance and impair driving performance. This is the first study correlating hypovigilance and driver performance in varied monotonous conditions, particularly on a short time scale (a few seconds). We induced vigilance decrement as assessed with an EEG during a monotonous driving simulator experiment. Road monotony was varied through both road design and road side variability. The driver's decrease in vigilance occurred due to both road design and road scenery monotony and almost independently of the driver's sensation seeking level. Such impairment was also correlated to observable measurements from the driver, the car and the environment. During periods of hypovigilance, the driving performance impairment affected lane positioning, time to lane crossing, blink frequency, heart rate variability and non-specific electrodermal response rates. This work lays the foundation for the development of an in-vehicle device preventing hypovigilance crashes on monotonous roads.
Fixing convergence of Gaussian belief propagation
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jason K [Los Alamos National Laboratory; Bickson, Danny [IBM RESEARCH LAB; Dolev, Danny [HEBREW UNIV
2009-01-01
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.
Convergence analysis for column-action methods in image reconstruction
DEFF Research Database (Denmark)
Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj
2016-01-01
. 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...
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.
Institute of Scientific and Technical Information of China (English)
丁锋
2016-01-01
In practice, one often encounters large-scale computational problems and optimization problems, so that the complexity, computation and computational accuracy of algorithms for solving these problems become a prominent issue, especially for the identification algorithms of large-scale nonlinear multi-variable systems. Therefore, the interesting research projects are proposed as follows: 1) the information filtering technology and the multi-innovation identification theory are used to study the identification methods for large-scale nonlinear systems, which can improve the identification accuracy;2) the hierarchical identification principle is used to study the hierarchical identification methods for multi-variable systems with high dimensionalities and more variables so as to reduce computational complexity;3) the martingale convergence theory is used to establish the convergence theory of the identification methods for nonlinear multi-variable systems;4) the parallel computing and the hierarchical computation are used to enhance the computational efficiency so as to solve the modeling problems of a class of large-scale nonlinear multi-variable systems.%实践中经常会遇到大型计算问题和优化问题，使得求解问题算法的复杂性、计算量和计算精度等成为突出问题，特别是大规模非线性多变量系统的辨识。对此，提出几个有趣的研究课题：1)利用信息滤波技术和多新息辨识理论研究能提高辨识精度的大规模系统辨识理论与方法；2)利用递阶辨识原理研究维数高、变量数目多、计算量小的多变量系统递阶辨识方法；3)利用鞅收敛理论建立非线性多变量系统辨识方法的收敛理论；4)利用并行计算与递阶计算技术提高辨识算法的计算效率，以解决一类大规模非线性多变量系统的模型化问题。
Estimating monotonic rates from biological data using local linear regression.
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.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
Gomez, Adrian
2010-01-01
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in the KPP-Fisher equation. We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Strong path convergence from Loewner driving convergence
Sheffield, Scott
2010-01-01
We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version applies in particular to random lattice paths that have chordal SLE as a scaling limit, with kappa less than 8 (non-space-filling). Existing SLE convergence proofs often begin by showing that the Loewner driving functions of these paths (viewed from infinity) converge to Brownian motion. Unfortunately, this is not sufficient, and additional arguments are required to complete the proofs. We show that driving function convergence is sufficient if it can be established for both parametrization directions and a generic target.
Institute of Scientific and Technical Information of China (English)
陆秋琴; 牛倩倩; 黄光球
2013-01-01
To solve large-scale optimization problems (OP) ,the algorithm with global convergence was constructed for solving OP based on the characteristics of memory principles(MP) and cellular automata(CA). In the algorithm, the theoretical search space of OP is divided into the discrete space,and the discrete space is defined as celullar space where each cell is an alternative solution of OP; the memorizing and forgeting rules of MP are used to control transition of states of each cell;a cellular state consists of position,increment of position and residual memory which is divided into three kinds of memory state such as instantaneous, short and long-term memory, each of which is strengthed or weakened by accepted stimulus strength, A cell is forgotted and then discarded when its residual memory is lower than a threshould. During evoluation process,a cell's transferring from one state to another realizes the search of cellular space on the theoretical search space. The stability condition of a reducible stochastic matrix was applied to prove the global convergence of the algorithm. The case study shows that the algorithm is efficient.%为了求解大规模优化问题,根据记忆原理与元胞自动机的特点构造了求解优化问题的全局收敛算法.在该算法中,将优化问题的理论搜索空间划分为离散搜索空间,该空间定义为元胞空间,其中的每个元胞对应着一个候选解.将记忆原理的记忆、遗忘规律用于控制每个元胞的状态转移；元胞的状态由其空间位置、位置修正量以及记忆残留值构成,该值分为瞬时记忆、短时记忆和长时记忆3种状态类型,并依据元胞接受刺激的强度被加强或衰减；记忆残留值低于某个阈值的元胞时被遗忘,不再被处理.在元胞演化过程中,元胞从一个状态转移到另一个状态实现了元胞空间对理论搜索空间的搜索.应用可归约随机矩阵的稳定性条件证明了本算法具有全局收敛性.
Vector optimization and monotone operators via convex duality recent advances
Grad, Sorin-Mihai
2014-01-01
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
Crespo Cuaresma, Jesus; Klasen, Stephan; Wacker, Konstantin M.
2016-01-01
Martin Ravallion ("Why Don't We See Poverty Convergence?" American Economic Review, 102(1): 504-23; 2012) presents evidence against the existence of convergence in global poverty rates despite convergence in household mean income levels and the close linkage between income growth and poverty reduction. We show that this finding is driven by a specification that demands more than simple convergence in poverty headcount rates and assumes a growth elasticity of poverty reduction, which is well-k...
Convergence S-compactifications
Directory of Open Access Journals (Sweden)
Bernd Losert
2014-07-01
Full Text Available Properties of continuous actions on convergence spaces are investigated. The primary focus is the characterization as to when a continuous action on a convergence space can be continuously extended to an action on a compactification of the convergence space. The largest and smallest such compactifications are studied.
Modeling non-monotone risk aversion using SAHARA utility functions
A. Chen; A. Pelsser; M. Vellekoop
2011-01-01
We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Directory of Open Access Journals (Sweden)
Ciepliński Krzysztof
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions of the functional equation , , where are closed intervals, and , are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
L^p solutions of reflected BSDEs under monotonicity condition
Rozkosz, Andrzej
2012-01-01
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by the penalization method. Our results are new even in the classical case p=2.
On Some Conjectures on the Monotonicity of Some Arithmetical Sequences
2012-01-01
THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES ∗ Florian Luca † Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089...visit of P. S. to the Centro de Ciencias Matemáticas de la UNAM in Morelia in August 2012. During the preparation of this paper, F. L. was supported in
Interval Routing and Minor-Monotone Graph Parameters
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 k
Multivariate Regression with Monotone Missing Observation of the Dependent Variables
Raats, V.M.; van der Genugten, B.B.; Moors, J.J.A.
2002-01-01
Multivariate regression is discussed, where the observations of the dependent variables are (monotone) missing completely at random; the explanatory variables are assumed to be completely observed.We discuss OLS-, GLS- and a certain form of E(stimated) GLS-estimation.It turns out that
Size monotonicity and stability of the core in hedonic games
Dimitrov, Dinko; Sung, Shao Chin
2011-01-01
We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games.
Monotone missing data and repeated controls of fallible authors
Raats, V.M.
2004-01-01
Chapters 2 and 3 focus on repeated audit controls with categorical variables. Chapter 4 and 5 introduce and analyse a very general multivariate regression model for (monotone) missing data. In the final Chapter 6 the previous chapters are combined into a more realistic model for repeated audit contr
Relaxing monotonicity in the identification of local average treatment effects
DEFF Research Database (Denmark)
Huber, Martin; Mellace, Giovanni
In heterogeneous treatment effect models with endogeneity, the identification of the local average treatment effect (LATE) typically relies on an instrument that satisfies two conditions: (i) joint independence of the potential post-instrument variables and the instrument and (ii) monotonicity...
Incorporating "Unconscious Reanalysis" into an Incremental, Monotonic Parser
Sturt, P
1995-01-01
This paper describes an implementation based on a recent model in the psycholinguistic literature. We define a parsing operation which allows the reanalysis of dependencies within an incremental and monotonic processing architecture, and discuss search strategies for its application in a head-initial language (English) and a head-final language (Japanese).
Interval Routing and Minor-Monotone Graph Parameters
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
Reasoning Biases, Non-Monotonic Logics, and Belief Revision
Dutilh Novaes, Catarina; Veluwenkamp, Herman
2017-01-01
A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science etc.: various logics (epistemic logics; non-monotonic logics), probabilistic systems (most notably, but not exclusi
Novel Newton's learning algorithm of neural networks
Institute of Scientific and Technical Information of China (English)
Long Ning; Zhang Fengli
2006-01-01
Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the gradient method is linearly convergent while Newton's method has second order convergence rate.The fast computing algorithm of Hesse matrix of the cost function of NN is proposed and it is the theory basis of the improvement of Newton's learning algorithm. Simulation results show that the convergence rate of Newton's learning algorithm is high and apparently faster than the traditional BP method's, and the robustness of Newton's learning algorithm is also better than BP method's.
Directory of Open Access Journals (Sweden)
Saewan Siwaporn
2011-01-01
Full Text Available Abstract In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works. 2000 MSC: 47H05; 47H09; 47H10.
A unified treatment of some iterative algorithms in signal processing and image reconstruction
Byrne, Charles
2004-02-01
Let T be a (possibly nonlinear) continuous operator on Hilbert space {\\cal H} . If, for some starting vector x, the orbit sequence {Tkx,k = 0,1,...} converges, then the limit z is a fixed point of T; that is, Tz = z. An operator N on a Hilbert space {\\cal H} is nonexpansive (ne) if, for each x and y in {\\cal H} , \\[ \\| Nx-Ny\\| \\leq \\| x-y\\|. \\] Even when N has fixed points the orbit sequence {Nkx} need not converge; consider the example N = -I, where I denotes the identity operator. However, for any \\alpha \\in (0,1) the iterative procedure defined by \\[ x^{k+1}=(1-\\alpha)x^k+\\alpha Nx^k \\] converges (weakly) to a fixed point of N whenever such points exist. This is the Krasnoselskii-Mann (KM) approach to finding fixed points of ne operators. A wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iterative procedure, for particular choices of the ne operator N. These include the Gerchberg-Papoulis method for bandlimited extrapolation, the SART algorithm of Anderson and Kak, the Landweber and projected Landweber algorithms, simultaneous and sequential methods for solving the convex feasibility problem, the ART and Cimmino methods for solving linear systems of equations, the CQ algorithm for solving the split feasibility problem and Dolidze's procedure for the variational inequality problem for monotone operators.
Non-monotonic effect of confinement on the glass transition
Varnik, Fathollah; Franosch, Thomas
2016-04-01
The relaxation dynamics of glass forming liquids and their structure are influenced in the vicinity of confining walls. This effect has mostly been observed to be a monotonic function of the slit width. Recently, a qualitatively new behaviour has been uncovered by Mittal and coworkers, who reported that the single particle dynamics in a hard-sphere fluid confined in a planar slit varies in a non-monotonic way as the slit width is decreased from five to roughly two particle diametres (Mittal et al 2008 Phys. Rev. Lett. 100 145901). In view of the great potential of this effect for applications in those fields of science and industry, where liquids occur under strong confinement (e.g. nano-technology), the number of researchers studying various aspects and consequences of this non-monotonic behaviour has been rapidly growing. This review aims at providing an overview of the research activity in this newly emerging field. We first briefly discuss how competing mechanisms such as packing effects and short-range attraction may lead to a non-monotonic glass transition scenario in the bulk. We then analyse confinement effects on the dynamics of fluids using a thermodynamic route which relates the single particle dynamics to the excess entropy. Moreover, relating the diffusive dynamics to the Widom’s insertion probability, the oscillations of the local dynamics with density at moderate densities are fairly well described. At high densities belonging to the supercooled regime, however, this approach breaks down signaling the onset of strongly collective effects. Indeed, confinement introduces a new length scale which in the limit of high densities and small pore sizes competes with the short-range local order of the fluid. This gives rise to a non-monotonic dependence of the packing structure on confinement, with a corresponding effect on the dynamics of structural relaxation. This non-monotonic effect occurs also in the case of a cone-plate type channel, where the degree
On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws
May, Georg
2016-01-01
We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone flux functions and a suitable shock-capturing operator are used. The main improvement, compared to previously published results of similar scope, is that no streamline-diffusion stabilization is used. This is the way discontinuous Galerkin schemes were originally proposed, and are most often used in practice.
A Hybrid Approach to Proving Memory Reference Monotonicity
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.
Measurement of non-monotonic Casimir forces between silicon nanostructures
Tang, L.; Wang, M.; Ng, C. Y.; Nikolic, M.; Chan, C. T.; Rodriguez, A. W.; Chan, H. B.
2017-01-01
Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field. Apart from controlling this force via the optical properties of materials, a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps. Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators, we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.
A Monotonic Precise Current DAC for Sensor Applications
Directory of Open Access Journals (Sweden)
P. Horsky
2008-12-01
Full Text Available In this paper a 17 bit monotonic precise current DAC for sensor applications is described. It is working in a harsh automotive environment in a wide temperature range with high output voltage swing and low current consumption. To guarantee monotonicity current division and segmentation techniques are used. To improve the output impedance, the accuracy and the voltage compliance of the DAC, two active cascoding loops and one follower loop are used. The resolution of the DAC is further increased by applying pulse width modulation to one fine LSB current. To achieve low power consumption unused coarse current sources are switched off. Several second order technological effects influencing final performance and circuits dealing with them are discussed.
Rational functions with maximal radius of absolute monotonicity
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.
Neural networks convergence using physicochemical data.
Karelson, Mati; Dobchev, Dimitar A; Kulshyn, Oleksandr V; Katritzky, Alan R
2006-01-01
An investigation of the neural network convergence and prediction based on three optimization algorithms, namely, Levenberg-Marquardt, conjugate gradient, and delta rule, is described. Several simulated neural networks built using the above three algorithms indicated that the Levenberg-Marquardt optimizer implemented as a back-propagation neural network converged faster than the other two algorithms and provides in most of the cases better prediction. These conclusions are based on eight physicochemical data sets, each with a significant number of compounds comparable to that usually used in the QSAR/QSPR modeling. The superiority of the Levenberg-Marquardt algorithm is revealed in terms of functional dependence of the change of the neural network weights with respect to the gradient of the error propagation as well as distribution of the weight values. The prediction of the models is assessed by the error of the validation sets not used in the training process.
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Directory of Open Access Journals (Sweden)
Krzysztof Ciepliński
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions φ:I→J of the functional equation φ(f(x=F(φ(x, x∈I, where I,J are closed intervals, and f:I→I, F:J→J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
Monotonic Property in Field Algebra of G-Spin Model
Institute of Scientific and Technical Information of China (English)
蒋立宁
2003-01-01
Let F be the field algebra of G-spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G. The paper builds a correspondence between D(H) and the D(H)-invariant sub-C*-algebra AH in F, and proves that the correspondence is strictly monotonic.
Modeling argumentation based semantics using non-monotonic reasoning
2005-01-01
Argumentation theory is an alternative style of formalizing non-monotonic reasoning. It seems, argumentation theory is a suitable framework for practical and uncertain reasoning, where arguments support conclusions. Dung's approach is an unifying framework which has played an influential role on argumentation research and Artificial Intelligence. Even though the success of the argumentation theory, it seems that argumentation theory is so far from being efficiently implemented like the logic ...
Institute of Scientific and Technical Information of China (English)
HE; Shanglu
2001-01-01
［1］Andersen, E. D., Ye, Y., On homogeneous algorithm for the monotone complementarity problem, Mathematical Programming, 1999, 84(2): 375.［2］Wright, S., Ralph, D., A supperlinear infeasible-interior-point algorithm for monotone complementarity problems, Mathematics of Operations Research, 1996, 24(4): 815.［3］Kojima, M., Noma, T., Yoshise, A., Global convergence in infeasible-interior-point algorithms, Mathematical Programming, 1994, 65(1): 43.［4］Kojima, M., Megiddo, N., Noma, T., A new continuation method for complementarity problems with uniform p-functions, Mathematical Programming, 1989, 43(1): 107.［5］Kojima, M., Megiddo, N., Mizuno, S., A general framework of continuation method for complementarity problems, Mathematics of Operations Research, 1993, 18(4): 945.［6］More, J., Rheinboldt, W., On P- and S-functions and related classes of n-dimensional nonlinear mappings, Linear Algebra and Its Applications, 1973, 6(1): 45.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
Gomez, Adrian; Trofimchuk, Sergei
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation u(t,x)=Δu(t,x)+u(t,x)(1-u(t-h,x)), u⩾0, x∈R. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in Eq. (*). We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch
Institute of Scientific and Technical Information of China (English)
Da-chuan Xu
2003-01-01
In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
Converged Registries Solution (CRS)
Department of Veterans Affairs — The Converged Registries platform is a hardware and software architecture designed to host individual patient registries and eliminate duplicative development effort...
Iterative Algorithms for Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
Yao Yonghong
2008-01-01
Full Text Available Abstract We suggest and analyze two new iterative algorithms for a nonexpansive mapping in Banach spaces. We prove that the proposed iterative algorithms converge strongly to some fixed point of .
Hierarchical Least Squares Identification and Its Convergence for Large Scale Multivariable Systems
Institute of Scientific and Technical Information of China (English)
丁锋; 丁韬
2002-01-01
The recursive least squares identification algorithm (RLS) for large scale multivariable systems requires a large amount of calculations, therefore, the RLS algorithm is difficult to implement on a computer. The computational load of estimation algorithms can be reduced using the hierarchical least squares identification algorithm (HLS) for large scale multivariable systems. The convergence analysis using the Martingale Convergence Theorem indicates that the parameter estimation error (PEE) given by the HLS algorithm is uniformly bounded without a persistent excitation signal and that the PEE consistently converges to zero for the persistent excitation condition. The HLS algorithm has a much lower computational load than the RLS algorithm.
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.
Non-monotonic reasoning in conceptual modeling and ontology design: A proposal
CSIR Research Space (South Africa)
Casini, G
2013-06-01
Full Text Available and modeling of defeasible information and non-monotonic reasoning services. Here we formalize a possible way of introducing non-monotonic reasoning into ORM2 schemas, enriching the language with special set of new constraints....
Foundations of genetic algorithms 1991
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
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.
Semantic Matchmaking as Non-Monotonic Reasoning: A Description Logic Approach
Di Noia, T; Donini, F M; 10.1613/jair.2153
2011-01-01
Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery.
Mixed Monotonicity of Partial First-In-First-Out Traffic Flow Models
Coogan, Samuel; Arcak, Murat; Kurzhanskiy, Alexander A.
2015-01-01
In vehicle traffic networks, congestion on one outgoing link of a diverging junction often impedes flow to other outgoing links, a phenomenon known as the first-in-first-out (FIFO) property. Simplified traffic models that do not account for the FIFO property result in monotone dynamics for which powerful analysis techniques exist. FIFO models are in general not monotone, but have been shown to be mixed monotone - a generalization of monotonicity that enables similarly powerful analysis techni...
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
Nikolaev, Evgeni V; Sontag, Eduardo D
2016-04-01
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, performed for a
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...
Munhoven, G.
2013-03-01
The total alkalinity-pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid-base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity-pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity-pH equation. This algorithm does not require any a priori knowledge of the solution. The iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10-15% compared to the fastest algorithm in our test series.
Convergence Analysis of a Domain Decomposition Paradigm
Energy Technology Data Exchange (ETDEWEB)
Bank, R E; Vassilevski, P S
2006-06-12
We describe a domain decomposition algorithm for use in several variants of the parallel adaptive meshing paradigm of Bank and Holst. This algorithm has low communication, makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. We show that for an idealized version of the algorithm, the rate of convergence is independent of both the global problem size N and the number of subdomains p used in the domain decomposition partition. Numerical examples illustrate the effectiveness of the procedure.
Monotonicity Formula and Regularity for General Free Discontinuity Problems
Bucur, Dorin; Luckhaus, Stephan
2014-02-01
We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d - 1. This result allows us to prove partial regularity results (that is closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi-Carriero-Leaci result for the Mumford-Shah functional.
The Non-Monotonic Effect of Financing Constraints on Investment
DEFF Research Database (Denmark)
Hirth, Stefan; Viswanatha, Marc
We analyze investment timing in a discrete-time framework with two possible investment dates, which is an extension of the model by Lyandres (2007). While Lyandres could only show non-monotonicity of investment in market frictions, we derive an investment threshold that is U-shaped in the firm's ......'s liquid funds, a result similar to the infinite-horizon model by Boyle and Guthrie (2003). However, due to the tractability of our model, we can more clearly explain the relevant trade-offs leading to the U-shape....
Contribution to the ergodic theory of piecewise monotone continuous maps
Faller, Bastien
2008-01-01
This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dynamical system. The principle of the coding is very similar to the one of expansion of real numbers. We first define the coding in a perspective similar to the one of the expansions of real numbers; this perspective was already adopted by Ré...
Stability of generalized monotonicity with respect to their characterizations
An, P T
2002-01-01
We show that known types of generalized monotone maps are not stable with respect to their characterizations (i.e., the characterizations are not maintained during an arbitrary map of this type is disturbed by an element with sufficiently small norm) then introduce s-quasimonotone maps, which are stable with respect to their characterization. For gradient maps, s-quasimonotonicity is related to s-quasiconvexity of the underlying function. A necessary and sufficient condition for a univariate polynomial to be s-quasimonotone is given. Furthermore, some stability properties of a-quasiconvex functions are presented.
Convergence of Fuzzy Set Sequences
Institute of Scientific and Technical Information of China (English)
FENG Yu-hu
2002-01-01
There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper,common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp or D*p, 1 ≤ p ＜∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comme nts on the convergence of LRfuzzy number sequences are represented.
A technique for accelerating the convergence of restarted GMRES
Energy Technology Data Exchange (ETDEWEB)
Baker, A H; Jessup, E R; Manteuffel, T
2004-03-09
We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.
A technique for accelerating the convergence of restarted GMRES
Energy Technology Data Exchange (ETDEWEB)
Baker, A H; Jessup, E R; Manteuffel, T
2004-03-09
We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.
Munhoven, G.
2013-08-01
The total alkalinity-pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid-base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity-pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity-pH equation. This algorithm does not require any a priori knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH Equations) provides reference implementations of several variants of the new algorithm in Fortran 90, together with new implementations of other, previously published solvers. The new iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10-15% compared to the fastest algorithm in our test series.
Noise can speed convergence in Markov chains.
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.
Stochastic Engine Convergence Diagnostics
Energy Technology Data Exchange (ETDEWEB)
Glaser, R
2001-12-11
The stochastic engine uses a Markov Chain Monte Carlo (MCMC) sampling device to allow an analyst to construct a reasonable estimate of the state of nature that is consistent with observed data and modeling assumptions. The key engine output is a sample from the posterior distribution, which is the conditional probability distribution of the state of nature, given the data. In applications the state of nature may refer to a complicated, multi-attributed feature like the lithology map of a volume of earth, or to a particular related parameter of interest, say the centroid of the largest contiguous sub-region of specified lithology type. The posterior distribution, which we will call f, can be thought of as the best stochastic description of the state of nature that incorporates all pertinent physical and theoretical models as well as observed data. Characterization of the posterior distribution is the primary goal in the Bayesian statistical paradigm. In applications of the stochastic engine, however, analytical calculation of the posterior distribution is precluded, and only a sample drawn from the distribution is feasible. The engine's MCMC technique, which employs the Metropolis-Hastings algorithm, provides a sample in the form of a sequence (chain) of possible states of nature, x{sup (1)}, x{sup (2)}, ..., x{sup (T)}, .... The sequencing is motivated by consideration of comparative likelihoods of the data. Asymptotic results ensure that the sample ultimately spans the entire posterior distribution and reveals the actual state frequencies that characterize the posterior. In mathematical jargon, the sample is an ergodic Markov chain with stationary distribution f. What this means is that once the chain has gone a sufficient number of steps, T{sub 0}, the (unconditional) distribution of the state, x{sup (T)}, at any step T {ge} T{sub 0} is the same (i.e., is ''stationary''), and is the posterior distribution, f. We call T{sub 0} the &apos
Testing monotonicity of a hazard: asymptotic distribution theory
Groeneboom, Piet
2011-01-01
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates, which use the monotonicity constraint, and either the empirical distribution function or the empirical cumulative hazard. They measure the excursions of the empirical estimates with respect to the isotonic estimates, due to local non-monotonicity. Asymptotic normality of the test statistics, if the hazard is strictly increasing on [0,a], is established under mild conditions. This is done by first approximating the global empirical distance by an distance with respect to the underlying distribution function. The resulting integral is treated as sum of increasingly many local integrals to which a CLT can be applied. The behavior of the local integrals is determined by a canonical process: the difference between the stochastic process x -> W(x)+x^2 where W is standard two-sid...
Nonaccommodative convergence excess.
von Noorden, G K; Avilla, C W
1986-01-15
Nonaccommodative convergence excess is a condition in which a patient has orthotropia or a small-angle esophoria or esotropia at distance and a large-angle esotropia at near, not significantly reduced by the addition of spherical plus lenses. The AC/A ratio, determined with the gradient method, is normal or subnormal. Tonic convergence is suspected of causing the convergence excess in these patients. Nonaccommodative convergence excess must be distinguished from esotropia with a high AC/A ratio and from hypoaccommodative esotropia. In 24 patients treated with recession of both medial recti muscles with and without posterior fixation or by posterior fixation alone, the mean correction of esotropia was 7.4 prism diopters at distance and 17 prism diopters at near.
Convergent Aeronautics Solutions Project
National Aeronautics and Space Administration — The Convergent Aeronautics Solutions (CAS) Project uses short-duration activities to establish early-stage concept and technology feasibility for high-potential...
Fixed mobile convergence handbook
Ahson, Syed A
2010-01-01
From basic concepts to future directions, this handbook provides technical information on all aspects of fixed-mobile convergence (FMC). The book examines such topics as integrated management architecture, business trends and strategic implications for service providers, personal area networks, mobile controlled handover methods, SIP-based session mobility, and supervisory and notification aggregator service. Case studies are used to illustrate technical and systematic implementation of unified and rationalized internet access by fixed-mobile network convergence. The text examines the technolo
Subsequential Convergence Conditions
Directory of Open Access Journals (Sweden)
Dik Mehmet
2007-01-01
Full Text Available Let be a sequence of real numbers and let be any regular limitable method. We prove that, under some assumptions, if a sequence or its generator sequence generated regularly by a sequence in a class of sequences is a subsequential convergence condition for , then for any integer , the repeated arithmetic means of , , generated regularly by a sequence in the class , is also a subsequential convergence condition for .
Energy Technology Data Exchange (ETDEWEB)
NONE
2012-12-15
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.
A proof of convergence of the concave-convex procedure using Zangwill's theory.
Sriperumbudur, Bharath K; Lanckriet, Gert R G
2012-06-01
The concave-convex procedure (CCCP) is an iterative algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms, including sparse support vector machines (SVMs), transductive SVMs, and sparse principal component analysis. Though CCCP is widely used in many applications, its convergence behavior has not gotten a lot of specific attention. Yuille and Rangarajan analyzed its convergence in their original paper; however, we believe the analysis is not complete. The convergence of CCCP can be derived from the convergence of the d.c. algorithm (DCA), proposed in the global optimization literature to solve general d.c. programs, whose proof relies on d.c. duality. In this note, we follow a different reasoning and show how Zangwill's global convergence theory of iterative algorithms provides a natural framework to prove the convergence of CCCP. This underlines Zangwill's theory as a powerful and general framework to deal with the convergence issues of iterative algorithms, after also being used to prove the convergence of algorithms like expectation-maximization and generalized alternating minimization. In this note, we provide a rigorous analysis of the convergence of CCCP by addressing two questions: When does CCCP find a local minimum or a stationary point of the d.c. program under consideration? and when does the sequence generated by CCCP converge? We also present an open problem on the issue of local convergence of CCCP.
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.
Institute of Scientific and Technical Information of China (English)
Tian-qi WU; Min YAO; Jian-hua YANG
2016-01-01
By adopting the distributed problem-solving strategy, swarm intelligence algorithms have been successfully applied to many optimization problems that are difficult to deal with using traditional methods. At present, there are many well-implemented algorithms, such as particle swarm optimization, genetic algorithm, artificial bee colony algorithm, and ant colony optimization. These algorithms have already shown favorable performances. However, with the objects becoming increasingly complex, it is becoming gradually more difficult for these algorithms to meet human’s demand in terms of accuracy and time. Designing a new algorithm to seek better solutions for optimization problems is becoming increasingly essential. Dolphins have many noteworthy biological characteristics and living habits such as echolocation, information exchanges, cooperation, and division of labor. Combining these biological characteristics and living habits with swarm intelligence and bringing them into optimization prob-lems, we propose a brand new algorithm named the ‘dolphin swarm algorithm’ in this paper. We also provide the definitions of the algorithm and specific descriptions of the four pivotal phases in the algorithm, which are the search phase, call phase, reception phase, and predation phase. Ten benchmark functions with different properties are tested using the dolphin swarm algorithm, particle swarm optimization, genetic algorithm, and artificial bee colony algorithm. The convergence rates and benchmark func-tion results of these four algorithms are compared to testify the effect of the dolphin swarm algorithm. The results show that in most cases, the dolphin swarm algorithm performs better. The dolphin swarm algorithm possesses some great features, such as first-slow-then-fast convergence, periodic convergence, local-optimum-free, and no specific demand on benchmark functions. Moreover, the dolphin swarm algorithm is particularly appropriate to optimization problems, with more
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.
Bandlimited image extrapolation with faster convergence
Cahana, D.; Stark, H.
1981-08-01
Techniques for increasing the convergence rate of the extrapolation algorithm proposed by Gerchberg (1974) and Papoulis (1975) for image restoration applications are presented. The techniques involve the modification of the Gerchberg-Papoulis algorithm to include additional a priori data such as the low-pass projection of the image either by the inclusion of the data at the start of the recursion to reduce the starting-point error, or by use of the low-pass image in each iteration to correct twice in the frequency domain. The performance of the GP algorithm and the two modifications presented in the restorations of a signal consisting of widely separated spectral components of equal magnitude and a signal with spectral components grouped in passbands is compared, and it is found that while both modifications reduced the starting point error, the convergence rate of the second technique was not substantially greater than that of the first despite the additional iterative frequency-plane correction. A significant improvement in the starting-point errors and convergence rates of both modified algorithms is obtained, however, when they are combined with adaptive thresholding in the presence of low noise levels and a signal with relatively well spaced impulse-type spectral components.
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Monotonic childhoods: representations of otherness in research writing
Directory of Open Access Journals (Sweden)
Denise Marcos Bussoletti
2011-12-01
Full Text Available This paper is part of a doctoral thesis entitled “Monotonic childhoods – a rhapsody of hope”. It follows the perspective of a critical psychosocial and cultural study, and aims at discussing the other’s representation in research writing, electing childhood as an allegorical and refl ective place. It takes into consideration, by means of analysis, the drawings and poems of children from the Terezin ghetto during the Second World War. The work is mostly based on Serge Moscovici’s Social Representation Theory, but it is also in constant dialogue with other theories and knowledge fi elds, especially Walter Benjamin’s and Mikhail Bakhtin’s contributions. At the end, the paper supports the thesis that conceives poetics as one of the translation axes of childhood cultures.
A COMPARISON OF DIFFERENT CONTRACTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
Bingsheng He; Xiang Wang; Junfeng Yang
2009-01-01
It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.
Parallel algorithms for unconstrained optimizations by multisplitting
Energy Technology Data Exchange (ETDEWEB)
He, Qing [Arizona State Univ., Tempe, AZ (United States)
1994-12-31
In this paper a new parallel iterative algorithm for unconstrained optimization using the idea of multisplitting is proposed. This algorithm uses the existing sequential algorithms without any parallelization. Some convergence and numerical results for this algorithm are presented. The experiments are performed on an Intel iPSC/860 Hyper Cube with 64 nodes. It is interesting that the sequential implementation on one node shows that if the problem is split properly, the algorithm converges much faster than one without splitting.
On A Rapidly Converging Series For The Riemann Zeta Function
Pichler, Alois
2012-01-01
To evaluate Riemann's zeta function is important for many investigations related to the area of number theory, and to have quickly converging series at hand in particular. We investigate a class of summation formulae and find, as a special case, a new proof of a rapidly converging series for the Riemann zeta function. The series converges in the entire complex plane, its rate of convergence being significantly faster than comparable representations, and so is a useful basis for evaluation algorithms. The evaluation of corresponding coefficients is not problematic, and precise convergence rates are elaborated in detail. The globally converging series obtained allow to reduce Riemann's hypothesis to similar properties on polynomials. And interestingly, Laguerre's polynomials form a kind of leitmotif through all sections.
A FILTER-TRUST-REGION METHOD FOR LC1 UNCONSTRAINED OPTIMIZATION AND ITS GLOBAL CONVERGENCE
Institute of Scientific and Technical Information of China (English)
Zhenghao Yang; Wenyu Sun; Chuangyin Dang
2008-01-01
In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative.We establish the global convergence of the algorithm under reasonable assumptions.
Energy Technology Data Exchange (ETDEWEB)
Gale, R. W.
1997-05-01
The likelihood of convergence in the electric power industry in Canada and the United Sates was examined, and the impact of such a development with respect to electricity and natural gas was explored. Based on developments to date, convergence between gas and electric utilities was considered an inevitable step towards the ultimate consolidation of the energy industry as a whole. Characteristics shared by gas and electric utilities were described, and likely developments leading to convergence of the two industries were reviewed. According to this author the competition between the opposing utilities will lead to price wars, loss leaders and other marketing strategies. Prices will be set by supply and demand principles. While users will be able to select customized, money-saving energy solutions, for suppliers, the new utility market will be a Darwinian battle royale, where only the most viable will survive. The end result will be a larger market dominated by a few super players.
Weak convergence theorems for a countable family of Lipschitzian mappings
Nilsrakoo, Weerayuth; Saejung, Satit
2009-08-01
This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We also establish weak convergence theorems for finding a common element of the set of fixed points, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain and improve the corresponding results recently proved by Moudafi [A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9 (2008) 37-43], Tada-Takahashi [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133 (2007) 359-370], and Plubtieng-Kumam [S. Plubtieng and P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings. J. Comput. Appl. Math. (2008) doi:10.1016/j.cam.2008.05.045]. Some of our results are established with weaker assumptions.
Rapidly converging multichannel controllers for broadband noise and vibrations
Berkhoff, A.P.
2010-01-01
Applications are given of a preconditioned adaptive algorithm for broadband multichannel active noise control. Based on state-space descriptions of the relevant transfer functions, the algorithm uses the inverse of the minimum-phase part of the secondary path in order to improve the speed of converg
Institute of Scientific and Technical Information of China (English)
王长钰; 屈彪
2003-01-01
The variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. Recently,Peng proposed a hybrid Newton-type method for minimizing the D-gap function.In this paper,a modification with generalized D-gap function gαβ of the method proposed by Peng is presented.It is shown that the algorithm has nice global convergence.This result here have improved and generalized those in the literature.Moreover, when the parameter β is chosen in a certain interval, it is proved that the generalized D-gap function gαβ has bounded level sets for the strongly monotone VIP. An error bound estimation of the algorithm is obtained.
Directory of Open Access Journals (Sweden)
Abdul Hameed Q. A. Al-Tai
2011-01-01
Full Text Available The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed (every real number r is replaced by a fuzzy number r¯ (either triangular fuzzy number or singleton fuzzy set (fuzzy point. And then, we will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence.
DEFF Research Database (Denmark)
Prasad, Ramjee; Ruggieri, Marina
2008-01-01
The paper focuses on the revolutionary changes that could characterise the future of networks. Those changes involve many aspects in the conceivement and exploitation of networks: architecture, services, technologies and modeling. The convergence of wired and wireless technologies along...... with the integration of system componennts and the convergence of services (e.g. communications and navigation) are only some of the elements that shape the perpsected mosaic. Authors delineate this vision, highlighting the presence of the space and stratospheric components and the related services as building block...
Strong Stationary Duality for M\\"obius Monotone Markov Chains: Unreliable Networks
Lorek, Pawel
2011-01-01
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\\"obius monotonicity of the chain. We show relations of M\\"obius monotonicity to other definitions of monotone chains. We give examples of dual chains in this context which have transitions only upwards. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an application to networks of queues.
The convergence of chaotic integrals
Bauer, O; Bauer, Oliver; Mainieri, Ronnie
1995-01-01
We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential.
Adaptive Alternating Minimization Algorithms
Niesen, Urs; Wornell, Gregory
2007-01-01
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables or equivalently of finding a point in the intersection of two sets. The iterative nature and simplicity of the algorithm has led to its application to many areas such as signal processing, information theory, control, and finance. A general set of sufficient conditions for the convergence and correctness of the algorithm is quite well-known when the underlying problem parameters are fixed. In many practical situations, however, the underlying problem parameters are changing over time, and the use of an adaptive algorithm is more appropriate. In this paper, we study such an adaptive version of the alternating minimization algorithm. As a main result of this paper, we provide a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm. Perhaps surprisingly, these conditions seem to be the minimal ones one would expect in ...
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.......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....
Non-monotonic dynamics and crosstalk in signaling pathways and their implications for pharmacology
van Wijk, Roeland; Tans, Sander J.; Wolde, Pieter Rein Ten; Mashaghi, Alireza
2015-06-01
Currently, drug discovery approaches commonly assume a monotonic dose-response relationship. However, the assumption of monotonicity is increasingly being challenged. Here we show that for two simple interacting linear signaling pathways that carry two different signals with different physiological responses, a non-monotonic input-output relation can arise with simple network topologies including coherent and incoherent feed-forward loops. We show that non-monotonicity of the response functions has severe implications for pharmacological treatment. Fundamental constraints are imposed on the effectiveness and toxicity of any drug independent of its chemical nature and selectivity due to the specific network structure.
Chakrabartty, Shantanu; Shaga, Ravi K; Aono, Kenji
2013-04-01
Analog circuits that are calibrated using digital-to-analog converters (DACs) use a digital signal processor-based algorithm for real-time adaptation and programming of system parameters. In this paper, we first show that this conventional framework for adaptation yields suboptimal calibration properties because of artifacts introduced by quantization noise. We then propose a novel online stochastic optimization algorithm called noise-shaping or ΣΔ gradient descent, which can shape the quantization noise out of the frequency regions spanning the parameter adaptation trajectories. As a result, the proposed algorithms demonstrate superior parameter search properties compared to floating-point gradient methods and better convergence properties than conventional quantized gradient-methods. In the second part of this paper, we apply the ΣΔ gradient descent algorithm to two examples of real-time digital calibration: 1) balancing and tracking of bias currents, and 2) frequency calibration of a band-pass Gm-C biquad filter biased in weak inversion. For each of these examples, the circuits have been prototyped in a 0.5-μm complementary metal-oxide-semiconductor process, and we demonstrate that the proposed algorithm is able to find the optimal solution even in the presence of spurious local minima, which are introduced by the nonlinear and non-monotonic response of calibration DACs.
Kolodzy, Janet; Grant, August E.; DeMars, Tony R.; Wilkinson, Jeffrey S.
2014-01-01
The emergence of the Internet, social media, and digital technologies in the twenty-first century accelerated an evolution in journalism and communication that fit under the broad term of convergence. That evolution changed the relationship between news producers and consumers. It broke down the geographical boundaries in defining our communities,…
Coghetto Roland
2015-01-01
We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).
DEFF Research Database (Denmark)
Prasad, Ramjee; Ruggieri, Marina
2008-01-01
with the integration of system componennts and the convergence of services (e.g. communications and navigation) are only some of the elements that shape the perpsected mosaic. Authors delineate this vision, highlighting the presence of the space and stratospheric components and the related services as building block...
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-09-01
Full Text Available We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections.
Language Convergence Infrastructure
V. Zaytsev (Vadim); J.M. Fernandes; R. Lämmel (Ralf); J.M.W. Visser (Joost); J. Saraiva
2011-01-01
htmlabstractThe process of grammar convergence involves grammar extraction and transformation for structural equivalence and contains a range of technical challenges. These need to be addressed in order for the method to deliver useful results. The paper describes a DSL and the infrastructure behind
Energy Technology Data Exchange (ETDEWEB)
Nevanlinna, O. [Helsinki Univ. of Technology, Espoo (Finland)
1994-12-31
This note summarizes some results on (a monitored version of) the Arnoldi method in Hilbert spaces. The interest in working in infinite dimensional spaces comes partly from the fact that only then can one have meaningful asymptotical statements (which hopefully give some light to the convergence of Arnoldi in large dimensional problems with iteration indices far less than the dimension).
Kolodzy, Janet; Grant, August E.; DeMars, Tony R.; Wilkinson, Jeffrey S.
2014-01-01
The emergence of the Internet, social media, and digital technologies in the twenty-first century accelerated an evolution in journalism and communication that fit under the broad term of convergence. That evolution changed the relationship between news producers and consumers. It broke down the geographical boundaries in defining our communities,…
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...
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...
Geometric Properties of the Monotonic Logical Grid Algorithm for Near Neighbor Calculations.
1986-04-24
ON * THE NEAR MISS PROBABILITY ................ o...................... 9 ANLSI F WPPNG (RANDOMPv MOTION)............................1.0 APPENDE...so near neighbor coming quite "close". It is these rare " near miss " events which’ r determine the required NNT size. Additional information concerning...34 near miss " probability. Such information .provides a criterion for optimizing (or minimizing) the NNT based on the ’cutoff radius" R, for the particular
A Filter Method for Nonlinear Semidefinite Programming with Global Convergence
Institute of Scientific and Technical Information of China (English)
Zhi Bin ZHU; Hua Li ZHU
2014-01-01
In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the suffi cient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is eff ective.
Demetriou, I. C.
2002-09-01
Methods are presented for least squares data smoothing by using the signs of divided differences of the smoothed values. Professor M.J.D. Powell initiated the subject in the early 1980s and since then, theory, algorithms and FORTRAN software make it applicable to several disciplines in various ways. Let us consider n data measurements of a univariate function which have been altered by random errors. Then it is usual for the divided differences of the measurements to show sign alterations, which are probably due to data errors. We make the least sum of squares change to the measurements, by requiring the sequence of divided differences of order m to have at most q sign changes for some prescribed integer q. The positions of the sign changes are integer variables of the optimization calculation, which implies a combinatorial problem whose solution can require about O(nq) quadratic programming calculations in n variables and n-m constraints. Suitable methods have been developed for the following cases. It has been found that a dynamic programming procedure can calculate the global minimum for the important cases of piecewise monotonicity m=1,q[greater-or-equal, slanted]1 and piecewise convexity/concavity m=2,q[greater-or-equal, slanted]1 of the smoothed values. The complexity of the procedure in the case of m=1 is O(n2+qn log2 n) computer operations, while it is reduced to only O(n) when q=0 (monotonicity) and q=1 (increasing/decreasing monotonicity). The case m=2,q[greater-or-equal, slanted]1 requires O(qn2) computer operations and n2 quadratic programming calculations, which is reduced to one and n-2 quadratic programming calculations when m=2,q=0, i.e. convexity, and m=2,q=1, i.e. convexity/concavity, respectively. Unfortunately, the technique that receives this efficiency cannot generalize for the highly nonlinear case m[greater-or-equal, slanted]3,q[greater-or-equal, slanted]2. However, the case m[greater-or-equal, slanted]3,q=0 is solved by a special strictly
Non-monotonicity of trace distance under tensor products
Energy Technology Data Exchange (ETDEWEB)
Maziero, Jonas, E-mail: jonas.maziero@ufsm.br [Universidade Federal de Santa Maria (UFSM), RS (Brazil). Departamento de Fisica
2015-10-15
The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article, we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not show up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states. (author)
Dynamical zeta functions for piecewise monotone maps of the interval
Ruelle, David
2004-01-01
Consider a space M, a map f:M\\to M, and a function g:M \\to {\\mathbb C}. The formal power series \\zeta (z) = \\exp \\sum ^\\infty _{m=1} \\frac {z^m}{m} \\sum _{x \\in \\mathrm {Fix}\\,f^m} \\prod ^{m-1}_{k=0} g (f^kx) yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval [0,1]. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of \\zeta (z) and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of (M,f,g).
Summable series and convergence factors
Moore, Charles N
1938-01-01
Fairly early in the development of the theory of summability of divergent series, the concept of convergence factors was recognized as of fundamental importance in the subject. One of the pioneers in this field was C. N. Moore, the author of the book under review.... Moore classifies convergence factors into two types. In type I he places the factors which have only the property that they preserve convergence for a convergent series or produce convergence for a summable series. In type II he places the factors which not only maintain or produce convergence but have the additional property that
A new algorithm for generalized fractional programming
Energy Technology Data Exchange (ETDEWEB)
Barros, A.; Frenk, J.B.G.; Schaible, S.; Zhang, S.
1994-12-31
A new algorithm for generalized fractional programs is introduced. This algorithm can be seen as {open_quotes}dual{close_quotes} to the Dinkelbach-type approach since it approximates the optimal value of the generalized fractional program from below. Convergence results as well as rate of convergence results are derived. An easy condition to achieve superlinear convergence of this new algorithm is also established. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm is superior to that of the generalized Dinkelbach type algorithm.
Generalized fractional programming and cutting plane algorithms
Energy Technology Data Exchange (ETDEWEB)
Frenk, J.B.G.
1994-12-31
A new algorithm for generalized fractional programs is introduced. This algorithm can be seen as {open_quotes}dual{close_quotes} to the Dinkelbach-type approach since it approximates the optimal value of the generalized fractional program from below. Convergence results as well as rate of convergence results are derived. An easy condition to achieve superlinear convergence of this new algorithm is also established. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm is superior to that of the generalized Dinkelbach-type algorithm.
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.
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 i
Effects of temperature on monotonic and fatigue properties of carbon fibre epoxy cross ply laminates
Matsuhisa, Y.; King, J.
1993-01-01
The effects of test temperature on damage accumulation behaviour has been studied using "Torayca" T800H / #3631 in conditions of monotonic and fatigue loading. The damage accumulation behaviour was found to vary as a function of the test temperature, with the effect of temperature on the damage behaviour being different between monotonic and fatigue loading.
Effects of temperature on monotonic and fatigue properties of carbon fibre epoxy cross ply laminates
Energy Technology Data Exchange (ETDEWEB)
Matsuhisa, Y. (Composite Materials Research Labs., Toray Industries Inc., Ehime (Japan)); King, J.E. (Composite Materials Research Labs., Toray Industries Inc., Ehime (Japan) Dept. of Materials Science and Metallurgy, Univ. of Cambridge (United Kingdom))
1993-11-01
The effects of test temperature on damage accumulation behaviour has been studied using ''Torayca'' T800H/[3631] in conditions of monotonic and fatigue loading. The damage accumulation behaviour was found to vary as a function of the test temperature, with the effect of temperature on the damage behaviour being different between monotonic and fatigue loading. (orig.).
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
Kovyrkina, O. A.; Ostapenko, V. V.
2016-05-01
The monotonicity of the CABARET scheme approximating a hyperbolic differential equation with a sign-changing characteristic field is analyzed. Monotonicity conditions for this scheme are obtained in domains where the characteristics have a sign-definite propagation velocity and near sonic lines, on which the propagation velocity changes its sign. These properties of the CABARET scheme are illustrated by test computations.
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 i
Computation of displacements for nonlinear elastic beam models using monotone iterations
Directory of Open Access Journals (Sweden)
Philip Korman
1988-01-01
Full Text Available We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present computations, which suggest efficiency of monotone methods for fourth order boundary value problems.
A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix
Shroff, Gautam
1989-01-01
A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.
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.
The Convergent Learning Space:
DEFF Research Database (Denmark)
Kjærgaard, Hanne Wacher; Kjeldsen, Lars Peter; Asmussen, Jørgen Bering
2013-01-01
is described as well as the theoretical construct and hypotheses surrounding the emergence of the concept in technology-rich classrooms, where students bring their own devices and involve their personal learning spaces and networks. The need for new ways of approaching concepts like choice, learning resources......This paper describes the concept of “The Convergent Learning Space” as it is being explored in an ongoing action research project carried out at undergraduate level in select bachelor programs at a Danish University College. The background nature, design, and beginning of this work in progress......, trajectories of participation etc. calls for new action and new pedagogies by teachers in order to secure alignment between students’ worlds and expectations and aims and plans of the teacher. Action research methods are being used to define and test the constituents and variables of the convergent learning...
Subsequential Convergence Conditions
Directory of Open Access Journals (Sweden)
İbrahim Çanak
2007-10-01
Full Text Available Let (un be a sequence of real numbers and let L be any (C,1 regular limitable method. We prove that, under some assumptions, if a sequence (un or its generator sequence (Vn(0(ÃŽÂ”u generated regularly by a sequence in a class Ã°ÂÂ’Âœ of sequences is a subsequential convergence condition for L, then for any integer mÃ¢Â‰Â¥1, the mth repeated arithmetic means of (Vn(0(ÃŽÂ”u, (Vn(m(ÃŽÂ”u, generated regularly by a sequence in the class Ã°ÂÂ’Âœ(m, is also a subsequential convergence condition for L.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Competition has been playing a dominant role among telecommunication equipment manufacturers. In 2006, however, merger overwhelmed competition. In the tide of converging, a large number of equipment manufacturers were involved in mergers. At the same time, telecommunication equipment manufacturers, the most innovative community in the world, drive 3G technology fast in line with its technical roadmap. In addition, Chinese equipment manufacturers cut a figure in world-class telecommunication markets, whic...
CONVERGENCE OF AN EXPLICIT UPWIND FINITE ELEMENT METHOD TO MULTI-DIMENSIONAL CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Jin-chao Xu; Lung-an Ying
2001-01-01
An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality.To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the Lp strong convergence of this scheme is proved.
Assessment of self-consistent field convergence in spin-dependent relativistic calculations
Nakano, Masahiko; Seino, Junji; Nakai, Hiromi
2016-07-01
This Letter assesses the self-consistent field (SCF) convergence behavior in the generalized Hartree-Fock (GHF) method. Four acceleration algorithms were implemented for efficient SCF convergence in the GHF method: the damping algorithm, the conventional direct inversion in the iterative subspace (DIIS), the energy-DIIS (EDIIS), and a combination of DIIS and EDIIS. Four different systems with varying complexity were used to investigate the SCF convergence using these algorithms, ranging from atomic systems to metal complexes. The numerical assessments demonstrated the effectiveness of a combination of DIIS and EDIIS for GHF calculations in comparison with the other discussed algorithms.
IT Convergence and Security 2012
Chung, Kyung-Yong
2013-01-01
The proceedings approaches the subject matter with problems in technical convergence and convergences of security technology. This approach is new because we look at new issues that arise from techniques converging. The general scope of the proceedings content is convergence security and the latest information technology. The intended readership are societies, enterprises, and research institutes, and intended content level is mid- to highly educated personals. The most important features and benefits of the proceedings are the introduction of the most recent information technology and its related ideas, applications and problems related to technology convergence, and its case studies and finally an introduction of converging existing security techniques through convergence security. Overall, through the proceedings, authors will be able to understand the most state of the art information strategies and technologies of convergence security.
Convergence analysis of a proximal Gauss-Newton method
Salzo, Saverio
2011-01-01
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applications for solving constrained nonlinear equations are discussed and the numerical performance of the method is assessed on some significant test problems.
Convergence analysis of Strang splitting for Vlasov-type equations
Einkemmer, Lukas
2012-01-01
A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step h. As an example, it is verified that the Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this analysis. Also, numerical experiments for the latter case are presented.
Convergence and Rate Analysis of Neural Networks for Sparse Approximation
Balavoine, Aurèle; Rozell, Christopher J
2011-01-01
We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal processing, but traditional analysis approaches are difficult because the objective functions are non-smooth. Specifically, we characterize the convergence properties of this system by showing that the LCA is globally convergent to a fixed point corresponding to the exact solution of the objective function, and (under some mild conditions) this solution is reached in finite time. Furthermore, we characterize the convergence rate of the system by showing that the LCA converges exponentially fast with an analytically bounded convergence rate (that depends on the specifics of a given problem). We support our analysis with several illustrative simulations.
Institute of Scientific and Technical Information of China (English)
李春景; 顾传青
2003-01-01
Two efficient recursive algorithms epsilon- algorithm and eta-algorithm are approximants were used to accelerate the convergence of the power series with functionvalued coefficients and to estimate characteristic value of the integral equations. Famous two algorithms.
Intensification and refraction of acoustical signals in partially choked converging ducts
Nayfeh, A. H.
1980-01-01
A computer code based on the wave-envelope technique is used to perform detailed numerical calculations for the intensification and refraction of sound in converging hard walled and lined circular ducts carrying high mean Mach number flows. The results show that converging ducts produce substantial refractions toward the duct center for waves propagating against near choked flows. As expected, the magnitude of the refraction decreases as the real part of the admittance increases. The pressure wave pattern is that of interference among the different modes, and hence the variation of the magnitude of pressure refraction with frequency is not monotonic.
Fused Lasso Screening Rules via the Monotonicity of Subdifferentials.
Wang, Jie; Fan, Wei; Ye, Jieping
2015-09-01
Fused Lasso is a popular regression technique that encodes the smoothness of the data. It has been applied successfully to many applications with a smooth feature structure. However, the computational cost of the existing solvers for fused Lasso is prohibitive when the feature dimension is extremely large. In this paper, we propose novel screening rules that are able to quickly identity the adjacent features with the same coefficients. As a result, the number of variables to be estimated can be significantly reduced, leading to substantial savings in computational cost and memory usage. To the best of our knowledge, the proposed approach is the first attempt to develop screening methods for the fused Lasso problem with general data matrix. Our major contributions are: 1) we derive a new dual formulation of fused Lasso that comes with several desirable properties; 2) we show that the new dual formulation of fused Lasso is equivalent to that of the standard Lasso by two affine transformations; 3) we propose a novel framework for developing effective and efficient screening rules for fused Lasso via the monotonicity of the subdifferentials (FLAMS). Some appealing features of FLAMS are: 1) our methods are safe in the sense that the detected adjacent features are guaranteed to have the same coefficients; 2) the dataset needs to be scanned only once to run the screening, whose computational cost is negligible compared to that of solving the fused Lasso; (3) FLAMS is independent of the solvers and can be integrated with any existing solvers. We have evaluated the proposed FLAMS rules on both synthetic and real datasets. The experiments indicate that FLAMS is very effective in identifying the adjacent features with the same coefficients. The speedup gained by FLAMS can be orders of magnitude.
Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups
Directory of Open Access Journals (Sweden)
Francesco Paolo Montefalcone
2010-12-01
Full Text Available Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S. We stress that S and @S are endowed with the homogeneous measures n????1 H and n????2 H , respectively, which are actually equivalent to the intrinsic (Q - 1-dimensional and (Q - 2-dimensional Hausdor measures with respect to a given homogeneous metric % on G. This result generalizes a classical inequality, involving the mean curvature of the hypersurface, proven by Michael and Simon [29] and Allard [1], independently. One may also deduce some related Sobolev-type inequalities. The strategy of the proof is inspired by the classical one and will be discussed at the rst section. After reminding some preliminary notions about Carnot groups, we shall begin by proving a linear isoperimetric inequality. The second step is a local monotonicity formula. Then we may achieve the proof by a covering argument.We stress however that there are many dierences, due to our non-Euclidean setting.Some of the tools developed ad hoc are, in order, a \\blow-up" theorem, which holds true also for characteristic points, and a smooth Coarea Formula for the HS-gradient. Other tools are the horizontal integration by parts formula and the 1st variation formula for the H-perimeter n????1H already developed in [30, 31] and then generalized to hypersurfaces having non-empty characteristic set in [32]. These results can be useful in the study of minimal and constant horizontal mean curvature hypersurfaces in Carnot groups.
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)
Immunity clone algorithm with particle swarm evolution
Institute of Scientific and Technical Information of China (English)
LIU Li-jue; CAI Zi-xing; CHEN Hong
2006-01-01
Combining the clonal selection mechanism of the immune system with the evolution equations of particle swarm optimization, an advanced algorithm was introduced for functions optimization. The advantages of this algorithm lies in two aspects.Via immunity operation, the diversity of the antibodies was maintained, and the speed of convergent was improved by using particle swarm evolution equations. Simulation programme and three functions were used to check the effect of the algorithm. The advanced algorithm were compared with clonal selection algorithm and particle swarm algorithm. The results show that this advanced algorithm can converge to the global optimum at a great rate in a given range, the performance of optimization is improved effectively.
NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Zuo Kongtian; Zhao Yudong; Chen Liping; Zhong Yifang; Huang Yuying
2005-01-01
A new hybrid MMA-MGCMMA (HMM) algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.
Knowledge Convergence and Collaborative Learning
Jeong, Heisawn; Chi, Michelene T. H.
2007-01-01
This paper operationalized the notion of knowledge convergence and assessed quantitatively how much knowledge convergence occurred during collaborative learning. Knowledge convergence was defined as an increase in common knowledge where common knowledge referred to the knowledge that all collaborating partners had. Twenty pairs of college students…
The Learning Convergence of CMAC in Cyclic Learning
Institute of Scientific and Technical Information of China (English)
姚殊; 张钹
1994-01-01
In this paper we discuss the learning convergence of the cerebellar model articulation controller (CMAC) in cyclic learning.We prove the following results.First,if the training samples are noiseless,the training algorithm converges if and only if the learning rate is chosen from (0,2).Second,when the training samples have noises,the learning algorithm will converge with a probability of one if the learning rate is dynamically decreased.Third,in the case with noises,with a small but fixed learning rate ε the mean square error of the weight sequences generated by the CMAC learning algorithm will be bounded by O(ε).Some simulation experiments are carried out to test these results.
A Self-Adaptive Fuzzy c-Means Algorithm for Determining the Optimal Number of Clusters
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
Design of the low area monotonic trim DAC in 40 nm CMOS technology for pixel readout chips
Drozd, A.; Szczygiel, R.; Maj, P.; Satlawa, T.; Grybos, P.
2014-12-01
The recent research in hybrid pixel detectors working in single photon counting mode focuses on nanometer or 3D technologies which allow making pixels smaller and implementing more complex solutions in each of the pixels. Usually single pixel in readout electronics for X-ray detection comprises of charge amplifier, shaper and discriminator that allow classification of events occurring at the detector as true or false hits by comparing amplitude of the signal obtained with threshold voltage, which minimizes the influence of noise effects. However, making the pixel size smaller often causes problems with pixel to pixel uniformity and additional effects like charge sharing become more visible. To improve channel-to-channel uniformity or implement an algorithm for charge sharing effect minimization, small area trimming DACs working in each pixel independently are necessary. However, meeting the requirement of small area often results in poor linearity and even non-monotonicity. In this paper we present a novel low-area thermometer coded 6-bit DAC implemented in 40 nm CMOS technology. Monte Carlo simulations were performed on the described design proving that under all conditions designed DAC is inherently monotonic. Presented DAC was implemented in the prototype readout chip with 432 pixels working in single photon counting mode, with two trimming DACs in each pixel. Each DAC occupies the area of 8 μm × 18.5 μm. Measurements and chips' tests were performed to obtain reliable statistical results.
Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control
Basin, Michael; Bharath Panathula, Chandrasekhara; Shtessel, Yuri
2016-09-01
This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.
Dualisation, decision lists and identification of monotone discrete functions
J.C. Bioch (Cor)
1998-01-01
textabstractMany data-analysis algorithms in machine learning, datamining and a variety of other disciplines essentially operate on discrete multi-attribute data sets. By means of discretisation or binarisation also numerical data sets can be successfully analysed. Therefore, in this paper we view/i
Dualisation, decision lists and identification of monotone discrete functions
J.C. Bioch (Cor)
1998-01-01
textabstractMany data-analysis algorithms in machine learning, datamining and a variety of other disciplines essentially operate on discrete multi-attribute data sets. By means of discretisation or binarisation also numerical data sets can be successfully analysed. Therefore, in this paper we