Convex Optimization without Projection Steps
Jaggi, Martin
2011-01-01
We study the general problem of minimizing a convex function over a compact convex domain. We will investigate a simple iterative approximation algorithm that does not need projection steps in order to stay inside the optimization domain. Instead of a projection step, the linearized problem defined by a current subgradient is solved, which gives a step direction that will naturally stay in the domain. The approach generalizes the sparse greedy algorithm of Clarkson (and the low-rank SDP solver by Hazan) to arbitrary convex domains, and to using subgradients for the case of non-differentiable convex functions. Analogously, we give a convergence proof guaranteeing {\\epsilon}-small duality gap after O(1/{\\epsilon}) iterations. The framework allows us understand the sparsity of approximate solutions for any l1-regularized convex optimization problem, expressed as a function of the approximation quality. We obtain matching upper and lower bounds of {\\Theta}(1/{\\epsilon}) for the sparsity for l1-problems. The same ...
Quantum information and convex optimization
Energy Technology Data Exchange (ETDEWEB)
Reimpell, Michael
2008-07-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
Conference on Convex Analysis and Global Optimization
Pardalos, Panos
2001-01-01
There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by th...
Convex analysis and global optimization
Tuy, Hoang
2016-01-01
This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints;
Finite dimensional convexity and optimization
Florenzano, Monique
2001-01-01
The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.
Convex analysis and optimization in Hadamard spaces
Bacak, Miroslav
2014-01-01
This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and optimization.
Non-convex multi-objective optimization
Pardalos, Panos M; Žilinskas, Julius
2017-01-01
Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in...
Directional Convexity and Finite Optimality Conditions.
1984-03-01
system, Necessary Conditions for optimality. Work Unit Number 5 (Optimization and Large Scale Systems) *Istituto di Matematica Applicata, Universita...that R(T) is convex would then imply x(u,T) e int R(T). Cletituto di Matematica Applicata, Universita di Padova, 35100 ITALY. Sponsored by the United
Optimal convex shapes for concave functionals
Bucur, Dorin; Lamboley, Jimmy
2011-01-01
Motivated by a long-standing conjecture of Polya and Szeg\\"o about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetriclike inequalities. As a byproduct of this approach we also obtain a quantitative version of the Kneser-S\\"uss inequality. Finally, for a large class of functionals involving Dirichlet energies and the surface measure, we perform a local analysis of strictly convex portions of the boundary via second order shape derivatives. This allows in particular to exclude the presence of smooth regions with positive Gauss curvature in an optimal shape for Polya-Szeg\\"o problem.
Reverse convex problems: an approach based on optimality conditions
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Ider Tseveendorj
2006-01-01
Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
Reverse convex problems: an approach based on optimality conditions
Ider Tseveendorj
2006-01-01
We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
A simple convex optimization problem with many applications
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
A Convex Optimization Approach to pMRI Reconstruction
Zhang, Cishen
2013-01-01
In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA, and another group of algorithms jointly compute the image and sensitivity functions by regularized optimization which is a non-convex problem with local only solutions. For the magnitude only image reconstruction, this paper derives a reconstruction formulation, which is linear in the magnitude image, and an associated convex hull in the solution space of the formulated equation containing the magnitude of the image. As a result, the magnitude only image reconstruction for pMRI is formulated into a two-step convex optimization problem, which has a globally optimal solution. An algorithm based on split-bregman and nuclear norm regularized optimizations is proposed to implement the two-step convex optimization and its applications to phantom and in-vi...
Global Optimization Approach to Non-convex Problems
Institute of Scientific and Technical Information of China (English)
LU Zi-fang; ZHENG Hui-li
2004-01-01
A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.
Global optimization over linear constraint non-convex programming problem
Institute of Scientific and Technical Information of China (English)
ZHANG Gui-Jun; WU Ti-Huan; YE Rong; YANG Hai-qing
2005-01-01
A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programmin g problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.
Closedness type regularity conditions in convex optimization and beyond
Directory of Open Access Journals (Sweden)
Sorin-Mihai Grad
2016-09-01
Full Text Available The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them.
Gradient of the Value Function in Parametric Convex Optimization Problems
Baotić, Mato
2016-01-01
We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange multipliers. In particular, we show that for the strictly convex parametric quadratic program the value function is continuously differentiable at every point in the interior of feasible space for which the Linear Independent Constraint Qualification holds.
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2017-01-01
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization prob...
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general...
Robust Quantum Error Correction via Convex Optimization
Kosut, R L; Lidar, D A
2007-01-01
Quantum error correction procedures have traditionally been developed for specific error models, and are not robust against uncertainty in the errors. Using a semidefinite program optimization approach we find high fidelity quantum error correction procedures which present robust encoding and recovery effective against significant uncertainty in the error system. We present numerical examples for 3, 5, and 7-qubit codes. Our approach requires as input a description of the error channel, which can be provided via quantum process tomography.
A Convex Optimization Model and Algorithm for Retinex
Directory of Open Access Journals (Sweden)
Qing-Nan Zhao
2017-01-01
Full Text Available Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components.
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.
A toolbox for robust PID controller tuning using convex optimization
Sadeghpour, Mehdi; de Oliveira, Vinicius; Karimi, Alireza
2012-01-01
A robust PID controller design toolbox for Matlab is presented in this paper. The design is based on linearizing or convexifying the conventional non-convex constraints on the classical robustness margins or H∞ constraints. Then the existing optimization solvers can be used to compute the controller parameters. The software can be used in a wide range of controller design problems, including multi-model systems and gain-scheduled controllers. The models can be parametric or non-parametric whi...
Optimal convex correcting procedures in problems of high dimension
Dokukin, A. A.; Senko, O. V.
2011-09-01
The properties of convex correcting procedures (CCPs) over sets of predictors are examined. It is shown that the minimization of the generalized error in a CCP is reduced to a quadratic programming problem. The conditions are studied under which a set of predictors cannot be reduced without degrading the accuracy of the corresponding optimal CCP. Experimental studies of the prognostic properties of CCPs for samples of one-dimensional linear regressions showed that CCP optimization can be an effective tool for regression variable selection.
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general....... They can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users. The results in this paper show that the power consumption of the pumps is reduced....
A Faster Algorithm for Quasi-convex Integer Polynomial Optimization
Hildebrand, Robert
2010-01-01
We present a faster exponential-time algorithm for integer optimization over quasi-convex polynomials. We study the minimization of a quasi-convex polynomial subject to s quasi-convex polynomial constraints and integrality constraints for all variables. The new algorithm is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time complexity is reached through applying a stronger ellipsoid rounding method and applying a recent advancement in the shortest vector problem to give a smaller exponential-time complexity of a Lenstra-type algorithm. For the bounded case, our algorithm attains a time-complexity of s (r l M d)^{O(1)} 2^{2n\\log_2(n) + O(n)} when M is a bound on the number of monomials in each polynomial and r is the binary encoding length of a bound on the feasible region. In the general case, s l^{O(1)} d^{O(n)} 2^{2n\\log_2(n)}. In each we assume d>=2 is a bound on the total degree of the polynomials and l bounds the maximum binary encoding size of the input...
A New Interpolation Approach for Linearly Constrained Convex Optimization
Espinoza, Francisco
2012-08-01
In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard\\'s interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton\\'s method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.
Identification of community structure in networks with convex optimization
Hildebrand, Roland
2008-01-01
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous one. A semidefinite relaxation of this conic program then allows to compute upper bounds on the maximum modularity of the network. Based on the solution of the corresponding semidefinite program, we design a randomized algorithm generating partitions of the network with suboptimal modularities. We apply this algorithm to several benchmark networks, demonstrating that it is competitive in accuracy with the best algorithms previously known. We use our method to provide the first proof of optimality of a partition for a real-world network.
Statistical Mechanics of Optimal Convex Inference in High Dimensions
Advani, Madhu; Ganguli, Surya
2016-07-01
A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α =(N /P )→∞ . However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α . We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than
Optimal Orthogonal Graph Drawing with Convex Bend Costs
Bläsius, Thomas; Wagner, Dorothea
2012-01-01
Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance. Moreover, as bend minimization over all planar embeddings is NP-hard, most approaches focus on a fixed planar embedding. We consider the problem OptimalFlexDraw that is defined as follows. Given a planar graph G on n vertices with maximum degree 4 and for each edge e a cost function cost_e : N_0 --> R defining costs depending on the number of bends on e, compute an orthogonal drawing of G of minimum cost. Note that this optimizes over all planar embeddings of the input graphs, and the cost functions allow fine-grained control on the bends of edges. In this generality OptimalFlexDraw is NP-hard. We show that it can be solved efficiently if 1) the cost function of each edge is convex and 2) the first bend on each edge does not cause any cost (which is a condition similar to the posi...
Optimization-based mesh correction with volume and convexity constraints
D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; Bochev, Pavel; Shashkov, Mikhail
2016-05-01
We consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.
A Localization Method for Multistatic SAR Based on Convex Optimization.
Directory of Open Access Journals (Sweden)
Xuqi Zhong
Full Text Available In traditional localization methods for Synthetic Aperture Radar (SAR, the bistatic range sum (BRS estimation and Doppler centroid estimation (DCE are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
A Localization Method for Multistatic SAR Based on Convex Optimization.
Zhong, Xuqi; Wu, Junjie; Yang, Jianyu; Sun, Zhichao; Huang, Yuling; Li, Zhongyu
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
First-order Convex Optimization Methods for Signal and Image Processing
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm
2012-01-01
In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple......-description problem. We finally present the contributions of the thesis. The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third...
Energy Technology Data Exchange (ETDEWEB)
Cho, Tae Min; Lee, Byung Chai [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2010-01-15
In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex approximations. In SORA, reliability estimation and deterministic optimization are performed sequentially. The sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the reliability analysis loop. In this study, the convex approximations for probabilistic constraint are constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. Hence, the proposed method requires much less function evaluations of probabilistic constraints in the deterministic optimization than the original SORA method. The efficiency and accuracy of the proposed method were verified through numerical examples
Asynchronous Code-Division Random Access Using Convex Optimization
Applebaum, Lorne; Duarte, Marco F; Calderbank, Robert
2011-01-01
Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel asynchronous (non-orthogonal) code-division random access scheme along with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time com...
Exploiting Symmetry in Integer Convex Optimization using Core Points
Herr, Katrin; Schürmann, Achill
2012-01-01
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. We define a core point of such a symmetry group as an integral point for which the convex hull of its orbit does not contain integral points other than the orbit points themselves. These core points allow us to decompose symmetric integer convex programming problems. Especially for symmetric integer linear programs we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of-the art commercial solvers and solve an open MIPLIB problem.
Institute of Scientific and Technical Information of China (English)
Qin Ni; Ch. Zillober; K. Schittkowski
2005-01-01
In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming (SCP). A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.
DEFF Research Database (Denmark)
Lauritzen, Niels
-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point...
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
Networked and Distributed Convex Optimization for Design, Estimation, and Verification
2009-10-01
IEEE Transactions on Automatic Control . 3...to appear in IEEE Transactions on Automatic Control , October 2009. 7. S. Joshi and S. Boyd, “Subspaces that Minimize the Condition Number of a Matrix...Jitter,” IEEE Transactions on Automatic Control , 54(3):652-657, March 2009. 16. A. Magnani and S. Boyd, “Convex Piecewise-Linear
Greedy vs. L1 convex optimization in sparse coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor;
2015-01-01
, such as face and action recognition, a comparative study of codes in abnormal event detection is less studied and hence no conclusion is gained on the effect of codes in detecting abnormalities. We constrict our comparison in two types of the above L0-norm solutions: greedy algorithms and convex L1-norm...
Pinson, Robin Marie
Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed
A proximal point method for nonsmooth convex optimization problems in Banach spaces
Directory of Open Access Journals (Sweden)
Y. I. Alber
1997-01-01
Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.
Fast Bundle-Level Type Methods for Unconstrained and Ball-Constrained Convex Optimization
2014-12-01
of half- spaces , hence it is convex and closed. Therefore, the subproblem (3.4) always has a unique solution as long as Qk is non-empty. To finish the...pixels in the image. The ‖u‖TV is convex and non-smooth. Table 5.1 Uniformly distributed QP instances A : n = 4000,m = 3000, L = 2.0e6, e0 = 2.89e4 Alg...generation. Mathematical pro- gramming, 118(1):177–206, 2009. [14] G. Lan. Bundle-level type methods uniformly optimal for smooth and non-smooth convex
Memoryless Routing in Convex Subdivisions: Random Walks are Optimal
Chen, Dan; Dujmovic, Vida; Morin, Pat
2009-01-01
A memoryless routing algorithm is one in which the decision about the next edge on the route to a vertex t for a packet currently located at vertex v is made based only on the coordinates of v, t, and the neighbourhood, N(v), of v. The current paper explores the limitations of such algorithms by showing that, for any (randomized) memoryless routing algorithm A, there exists a convex subdivision on which A takes Omega(n^2) expected time to route a message between some pair of vertices. Since this lower bound is matched by a random walk, this result implies that the geometric information available in convex subdivisions is not helpful for this class of routing algorithms. The current paper also shows the existence of triangulations for which the Random-Compass algorithm proposed by Bose etal (2002,2004) requires 2^{\\Omega(n)} time to route between some pair of vertices.
A recurrent neural network for solving a class of generalized convex optimization problems.
Hosseini, Alireza; Wang, Jun; Hosseini, S Mohammad
2013-08-01
In this paper, we propose a penalty-based recurrent neural network for solving a class of constrained optimization problems with generalized convex objective functions. The model has a simple structure described by using a differential inclusion. It is also applicable for any nonsmooth optimization problem with affine equality and convex inequality constraints, provided that the objective function is regular and pseudoconvex on feasible region of the problem. It is proven herein that the state vector of the proposed neural network globally converges to and stays thereafter in the feasible region in finite time, and converges to the optimal solution set of the problem.
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints
Mahdavi, Mehrdad; Yang, Tianbao
2011-01-01
In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set $\\mathcal{K}$ from which the decisions are made. While for simple shapes (e.g. Euclidean ball) the projection is straightforward, for arbitrary complex sets this is the main computational challenge and may be inefficient in practice. In this paper, we consider an alternative online convex optimization problem. Instead of requiring decisions belong to $\\mathcal{K}$ for all rounds, we only require that the constraints which define the set $\\mathcal{K}$ be satisfied in the long run. We show that our framework can be utilized to solve a relaxed version of online learning with side constraints addressed in \\cite{DBLP:conf/colt/MannorT06} and \\cite{DBLP:conf/aaai/KvetonYTM08}. By turning the problem into an online convex-concave optimization problem, we propose an efficient algo...
Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.
Hoffmann, Aswin L; Siem, Alex Y D; den Hertog, Dick; Kaanders, Johannes H A M; Huizenga, Henk
2006-12-21
In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.
Optimal placement of convex polygons to maximize point containment
Energy Technology Data Exchange (ETDEWEB)
Dickerson, M. [Middlebury College, VT (United States); Scharstein, D. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a placement of P that contains the maximum number of points in S. We allow both translation and rotation. Our algorithm is self-contained and utilizes the geometric properties of the containing regions in the parameter space of transformations. The algorithm requires O(nk{sup 2} m{sup 2} log(mk)) time and O(n + m) space, where k is the maximum number of points contained. This provides a linear improvement over the best previously known algorithm when k is large ({Theta}(n)) and a cubic improvement when k is small. We also show that the algorithm can be extended to solve bichromatic and general weighted variants of the problem.
Convex optimization approach to the fusion of identity information
Li, Lingjie; Luo, Zhi-Quan; Wong, Kon M.; Bosse, Eloi
1999-03-01
We consider the problem of identity fusion for a multi- sensor target tracking system whereby sensors generate reports on the target identities. Since the sensor reports are typically fuzzy, 'incomplete' and inconsistent, the fusion approach based on the minimization of inconsistencies between the sensor reports by using a convex Quadratic Programming (QP) and linear programming (LP) formulation. In contrast to the Dempster-Shafer's evidential reasoning approach which suffers from exponentially growing completely, our approach is highly efficient. Moreover, our approach is capable of fusing 'ratio type' sensor reports, thus it is more general than the evidential reasoning theory. When the sensor reports are consistent, the solution generated by the new fusion method can be shown to converge to the true probability distribution. Simulation work shows that our method generates reasonable fusion results, and when only 'Subset type' sensor reports are presented, it produces fusion results similar to that obtained via the evidential reasoning theory.
Greedy vs. L1 Convex Optimization in Sparse Coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor
Sparse representation has been applied successfully in many image analysis applications, including abnormal event detection, in which a baseline is to learn a dictionary from the training data and detect anomalies from its sparse codes. During this procedure, sparse codes which can be achieved...... and action recognition, a comparative study of codes in abnormal event detection is less studied and hence no conclusion is gained on the effect of codes in detecting abnormalities. We constrict our comparison in two types of the above L0-norm solutions: greedy algorithms and convex L1-norm solutions....... Considering the property of abnormal event detection, i.e., only normal videos are used as training data due to practical reasons, effective codes in classification application may not perform well in abnormality detection. Therefore, we compare the sparse codes and comprehensively evaluate their performance...
Craft, David
2010-10-01
A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets.
Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization
Adhikari, Sam
2007-11-01
Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.
Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization
Directory of Open Access Journals (Sweden)
Guo Ye-Cai
2017-01-01
Full Text Available Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.
Implementation of an optimal first-order method for strongly convex total variation regularization
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm; Jørgensen, Jakob Heide; Hansen, Per Christian;
2012-01-01
We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to μ-strongly convex objective functions with L-Lipschitz continuous gradient...
Optimal Energy Consumption in Refrigeration Systems - Modelling and Non-Convex Optimisation
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Skovrup, Morten J.
2012-01-01
that is somewhat more efficient than general purpose optimisation algorithms for NMPC and still near to optimal. Since the non-convex cost function has multiple extrema, standard methods for optimisation cannot be directly applied. A qualitative analysis of the system's constraints is presented and a unique...
Convex Array Vector Velocity Imaging Using Transverse Oscillation and Its Optimization
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Brandt, Andreas Hjelm; Bachmann Nielsen, Michael
2015-01-01
A method for obtaining vector flow images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields and evaluates their performance using simulations and measurements with an experimental scanner. A 3-MHz 192-element conve...
An uncertain multidisciplinary design optimization method using interval convex models
Li, Fangyi; Luo, Zhen; Sun, Guangyong; Zhang, Nong
2013-06-01
This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss-Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.
Bot, Radu Ioan
2012-01-01
The aim of this paper is to develop an efficient algorithm for solving a class of unconstrained nondifferentiable convex optimization problems in finite dimensional spaces. To this end we formulate first its Fenchel dual problem and regularize it in two steps into a differentiable strongly convex one with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method with the aim of accelerating the resulting convergence scheme. The theoretical results are finally applied to an l1 regularization problem arising in image processing.
Convex relaxation of Optimal Power Flow in Distribution Feeders with embedded solar power
DEFF Research Database (Denmark)
Hermann, Alexander Niels August; Wu, Qiuwei; Huang, Shaojun
2016-01-01
panels with uncontrolled inverters, the upper limit of installable capacity is quickly reached in many of today’s distribution feeders. This problem can often be mitigated by optimally controlling the voltage angles of inverters. However, the optimal power flow problem in its standard form is a large......There is an increasing interest in using Distributed Energy Resources (DER) directly coupled to end user distribution feeders. This poses an array of challenges because most of today’s distribution feeders are designed for unidirectional power flow. Therefore when installing DERs such as solar...... scale non-convex optimization problem, and thus can’t be solved precisely and also is computationally heavy and intractable for large systems. This paper examines the use of a convex relaxation using Semi-definite programming to optimally control solar power inverters in a distribution grid in order...
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application......The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...
Reconstruction of the early Universe as a convex optimization problem
Brenier, Y.; Frisch, U.; Hénon, M.; Loeper, G.; Matarrese, S.; Mohayaee, R.; Sobolevskiĭ, A.
2003-12-01
We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales - a few Mpc - where multistreaming becomes significant. Above 6 h-1 Mpc we propose and implement an effective Monge-Ampère-Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O(N3) time complexity and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60 per cent of exactly reconstructed points. We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge-Ampère equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.
Exact Convex Relaxation of Optimal Power Flow in Radial Networks
Energy Technology Data Exchange (ETDEWEB)
Gan, LW; Li, N; Topcu, U; Low, SH
2015-01-01
The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.
Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging
Girard, Julien N; Starck, Jean Luc; Corbel, Stéphane; Woiselle, Arnaud; Tasse, Cyril; McKean, John P; Bobin, Jérôme
2015-01-01
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emissions as compared to CLEAN. With the advent of large radiotel...
On the acceleration of the double smoothing technique for unconstrained convex optimization problems
Bot, Radu Ioan
2012-01-01
In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the Fenchel dual problem associated to the problem to be solved into an optimization problem having a differentiable strongly convex objective function with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method. The aim of this paper is to show how do the properties of the functions in the objective of the primal problem influence the implementation of the double smoothing approach and its rate of convergence. The theoretical results are applied to linear inverse problems by making use of different regularization functionals.
Acho, Sussan Nkwenti; Rae, William Ian Duncombe
2016-10-01
A convex active contour model requires a predefined threshold value to determine the global solution for the best contour to use when doing mass segmentation. Fixed thresholds or manual tuning of threshold values for optimum mass boundary delineation are impracticable. A proposed method is presented to determine an optimized mass-specific threshold value for the convex active contour derived from the probability matrix of the mass with the particle swarm optimization method. We compared our results with the Chan-Vese segmentation and a published global segmentation model on masses detected on direct digital mammograms. The regional term of the convex active contour model maximizes the posterior partitioning probability for binary segmentation. Suppose the probability matrix is binary thresholded using the particle swarm optimization to obtain a value T1, we define the optimal threshold value for the global minimizer of the convex active contour as the mean intensity of all pixels whose probabilities are greater than T1. The mean Jaccard similarity indices were 0.89±0.07 for the proposed/Chan-Vese method and 0.88±0.06 for the proposed/published segmentation model. The mean Euclidean distance between Fourier descriptors of the segmented areas was 0.05±0.03 for the proposed/Chan-Vese method and 0.06±0.04 for the proposed/published segmentation model. This efficient method avoids problems of initial level set contour placement and contour re-initialization. Moreover, optimum segmentation results are realized for all masses improving on the fixed threshold value of 0.5 proposed elsewhere. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
A New Subspace Correction Method for Nonlinear Unconstrained Convex Optimization Problems
Institute of Scientific and Technical Information of China (English)
Rong-liang CHEN; Jin-ping ZENG
2012-01-01
This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S.Nash in 2000 and the subspace correction algorithm proposed by X.Tai and J.Xu in 2001.Under some reasonable assumptions,we obtain the convergence as well as a convergence rate estimate for the algorithm.Numerical results show that the algorithm is effective.
Convex and Network Flow Optimization for Structured Sparsity
Mairal, Julien; Obozinski, Guillaume; Bach, Francis
2011-01-01
We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2 or l_infinity norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l_infinity norms can be computed exactly in polynomial time by solving a quadratic minimum cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such a...
Reconstruction of the early Universe as a convex optimization problem
Brenier, Y; Hénon, M; Loeper, G; Matarrese, S; Mohayaee, R; Sobolevskii, A
2003-01-01
We show that the deterministic past history of the Universe can be uniquely reconstructed from the knowledge of the present mass density field, the latter being inferred from the 3D distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales -- a few Mpc -- where multi-streaming becomes significant. Above 6 Mpc/h we propose and implement an effective Monge-Ampere-Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge (1781). After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than cubic time complexity in N and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60% of exactly reconstructed points. We apply several interrelated tools f...
A two-layer recurrent neural network for nonsmooth convex optimization problems.
Qin, Sitian; Xue, Xiaoping
2015-06-01
In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush-Kuhn-Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems.
Botelho, Fabio
2014-01-01
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo
2016-11-01
We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.
Institute of Scientific and Technical Information of China (English)
雷耀斌; 吴让泉
2001-01-01
We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset of Ra, and in the presence of a higher interest rate for borrowing. The setting is that of a continuous-time, Ito process model for the underlying asset prices. The solution of the unconstrained problem is given. In addition to the original constrained optimization problem, a so-called combined dual problem is introduced. Finally, the existence question of optimal processes for both the dual and the primal problem is settled.
A convex programming framework for optimal and bounded suboptimal well field management
DEFF Research Database (Denmark)
Dorini, Gianluca Fabio; Thordarson, Fannar Ørn; Bauer-Gottwein, Peter
2012-01-01
are often convex, hence global optimality can be attained by a wealth of algorithms. Among these, the Interior Point methods are extensively employed for practical applications, as they are capable of efficiently solving large-scale problems. Despite this, management models explicitly embedding both systems....... The objective of the management is to minimize the total cost of pump operations over a multistep time horizon, while fulfilling a set of time-varying management constraints. Optimization in groundwater management and pressurized WDNs have been widely investigated in the literature. Problem formulations...
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Directory of Open Access Journals (Sweden)
Chuancun Yin
2015-01-01
Full Text Available We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.
Directory of Open Access Journals (Sweden)
Tobias Nüesch
2014-02-01
Full Text Available This paper presents a novel method to solve the energy management problem for hybrid electric vehicles (HEVs with engine start and gearshift costs. The method is based on a combination of deterministic dynamic programming (DP and convex optimization. As demonstrated in a case study, the method yields globally optimal results while returning the solution in much less time than the conventional DP method. In addition, the proposed method handles state constraints, which allows for the application to scenarios where the battery state of charge (SOC reaches its boundaries.
Gradient vs. approximation design optimization techniques in low-dimensional convex problems
Fedorik, Filip
2013-10-01
Design Optimization methods' application in structural designing represents a suitable manner for efficient designs of practical problems. The optimization techniques' implementation into multi-physical softwares permits designers to utilize them in a wide range of engineering problems. These methods are usually based on modified mathematical programming techniques and/or their combinations to improve universality and robustness for various human and technical problems. The presented paper deals with the analysis of optimization methods and tools within the frame of one to three-dimensional strictly convex optimization problems, which represent a component of the Design Optimization module in the Ansys program. The First Order method, based on combination of steepest descent and conjugate gradient method, and Supbproblem Approximation method, which uses approximation of dependent variables' functions, accompanying with facilitation of Random, Sweep, Factorial and Gradient Tools, are analyzed, where in different characteristics of the methods are observed.
Institute of Scientific and Technical Information of China (English)
ZHU Detong
2000-01-01
This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems.The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature.A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions.The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.
An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control
Dinh, Quoc Tran; Diehl, Moritz
2012-01-01
In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite convex approximations via a parameterization technique. This leads to an iterative procedure to search a local optimum of the nonconvex problem. The convergence of the algorithm is analyzed under mild assumptions. Applications in static output feedback control are benchmarked and numerical tests are implemented based on the data from the COMPLeib library.
Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost
Institute of Scientific and Technical Information of China (English)
Da-cheng YAO
2013-01-01
We study an inventory system in which products are ordered from outside to meet demands,and the cumulative demand is governed by a Brownian motion.Excessive demand is backlogged.We suppose that the shortage and holding costs associated with the inventory are given by a general convex function.The product ordering from outside incurs a linear ordering cost and a setup fee.There is a constant leadtime when placing an order.The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.
Institute of Scientific and Technical Information of China (English)
ZHANG Qing-xiang; ZHANG Yong-zhan
2013-01-01
The definition of generalized unified (C,α,p,d)-convex function is given.The concepts of generalized unified (C,α,p,d)-quasiconvexity,generalized unified (C,α,p,d)-pseudoconvexity and generalized unified (C,α,p,d)-strictly pseudoconvex functions are presented.The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.
Lateral ventricle segmentation of 3D pre-term neonates US using convex optimization.
Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; Ukwatta, Eranga; Fenster, Aaron
2013-01-01
Intraventricular hemorrhage (IVH) is a common disease among preterm infants with an occurrence of 12-20% in those born at less than 35 weeks gestational age. Neonates at risk of IVH are monitored by conventional 2D ultrasound (US) for hemorrhage and potential ventricular dilation. Compared to 2D US relying on linear measurements from a single slice and visually estimates to determine ventricular dilation, 3D US can provide volumetric ventricle measurements, more sensitive to longitudinal changes in ventricular volume. In this work, we propose a global optimization-based surface evolution approach to the segmentation of the lateral ventricles in preterm neonates with IVH. The proposed segmentation approach makes use of convex optimization technique in combination with a subject-specific shape model. We show that the introduced challenging combinatorial optimization problem can be solved globally by means of convex relaxation. In this regard, we propose a coupled continuous max-flow model, which derives a new and efficient dual based algorithm, that can be implemented on GPUs to achieve a high-performance in numerics. Experiments demonstrate the advantages of our approach in both accuracy and efficiency. To the best of our knowledge, this paper reports the first study on semi-automatic segmentation of lateral ventricles in neonates with IVH from 3D US images.
Zhao, Dang-Jun; Song, Zheng-Yu
2017-08-01
This study proposes a multiphase convex programming approach for rapid reentry trajectory generation that satisfies path, waypoint and no-fly zone (NFZ) constraints on Common Aerial Vehicles (CAVs). Because the time when the vehicle reaches the waypoint is unknown, the trajectory of the vehicle is divided into several phases according to the prescribed waypoints, rendering a multiphase optimization problem with free final time. Due to the requirement of rapidity, the minimum flight time of each phase index is preferred over other indices in this research. The sequential linearization is used to approximate the nonlinear dynamics of the vehicle as well as the nonlinear concave path constraints on the heat rate, dynamic pressure, and normal load; meanwhile, the convexification techniques are proposed to relax the concave constraints on control variables. Next, the original multiphase optimization problem is reformulated as a standard second-order convex programming problem. Theoretical analysis is conducted to show that the original problem and the converted problem have the same solution. Numerical results are presented to demonstrate that the proposed approach is efficient and effective.
Higher-order principal component pursuit via tensor approximation and convex optimization
Institute of Scientific and Technical Information of China (English)
Sijia Cai; Ping Wang; Linhao Li; Chuhan Zhang
2014-01-01
Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit (HOPCP), since it is critical in multi-way data analysis. Unlike the convexification (nuclear norm) for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme: the augmented Lagrangian alternating di-rection method (ALADM) and its truncated higher-order singular value decomposition (ALADM-THOSVD) version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computational y intractable problems. Experimental re-sults on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.
Rotationally resliced 3D prostate TRUS segmentation using convex optimization with shape priors.
Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Fenster, Aaron
2015-02-01
Efficient and accurate segmentations of 3D end-firing transrectal ultrasound (TRUS) images play an important role in planning of 3D TRUS guided prostate biopsy. However, poor image quality of the input 3D TRUS images, such as strong imaging artifacts and speckles, often makes it a challenging task to extract the prostate boundaries accurately and efficiently. In this paper, the authors propose a novel convex optimization-based approach to delineate the prostate surface from a given 3D TRUS image, which reduces the original 3D segmentation problem to a sequence of simple 2D segmentation subproblems over the rotational reslices of the 3D TRUS volume. Essentially, the authors introduce a novel convex relaxation-based contour evolution approach to each 2D slicewise image segmentation with the joint optimization of shape information, where the learned 2D nonlinear statistical shape prior is incorporated to segment the initial slice, its result is propagated as a shape constraint to the segmentation of the following slices. In practice, the proposed segmentation algorithm is implemented on a GPU to achieve the high computational performance. Experimental results using 30 patient 3D TRUS images show that the proposed method can achieve a mean Dice similarity coefficient of 93.4% ± 2.2% in 20 s for one 3D image, outperforming the existing local-optimization-based methods, e.g., level-set and active-contour, in terms of accuracy and efficiency. In addition, inter- and intraobserver variability experiments show its good reproducibility. A semiautomatic segmentation approach is proposed and evaluated to extract the prostate boundary from 3D TRUS images acquired by a 3D end-firing TRUS guided prostate biopsy system. Experimental results suggest that it may be suitable for the clinical use involving the image guided prostate biopsy procedures.
Directory of Open Access Journals (Sweden)
Akemi Gálvez
2013-01-01
Full Text Available Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.
Engberg, Lovisa; Forsgren, Anders; Hårdemark, Björn
2016-01-01
Given the widespread agreement that doses-at-volume play important roles in quality assessment of radiation therapy treatment plans, planning objectives that correlate well with explicit dose-at-volume optimization are likely to correlate well with plan quality. In this study, planning objectives are formulated to explicitly either minimize or maximize convex approximations of dose-at-volume, namely, mean-tail-doses. This is in contrast to the conventionally used planning objectives, which are used to maximize clinical goal fulfilment by relating to deviations from dose-at-volume thresholds. Advantages of the proposed planning objectives are investigated through juxtaposition with conventional objectives in a computational study of two patient cases, each with three doses-at-volume to be minimized subject to PTV coverage. With proposed planning objectives, this is translated into minimizing three mean-tail-doses. Comparison with conventional objectives is carried out in the dose-at-volume domain and in the no...
libCreme: An optimization library for evaluating convex-roof entanglement measures
Röthlisberger, Beat; Loss, Daniel
2011-01-01
We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focussing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems.
Evaluation of Advanced Control for Li-ion Battery Balancing Systems using Convex Optimization
DEFF Research Database (Denmark)
Pinto, Claudio; Barreras, Jorge Varela; Schaltz, Erik
2016-01-01
of energy losses, available capacity or temperature are obtained for the last three categories, even for moderate balancing currents. In particular, remarkable improvements are observed under conditions of high power demand with high variability, i.e., smaller battery sizes and more demanding driving cycles....... systems are evaluated in this paper by means of convex optimization. More than one hundred cases in a pure EV application are evaluated. Balancing circuits' efficiency models are implemented and realistic cell-to-cell parameter distributions are considered based on experimental data. Different battery...... sizes and driving cycles are considered. Balancing circuit topology is taken into account by selecting a specific category of energy transfer: cell-to-heat, bypass, cell-to-pack, pack-to-cell, cell-to-cell shared, cell-to-cell distributed or cell-to-pack-to-cell. In general, better results in terms...
Wei, W. B.; Tan, L.; Jia, M. Q.; Pan, Z. K.
2017-01-01
The variational level set method is one of the main methods of image segmentation. Due to signed distance functions as level sets have to keep the nature of the functions through numerical remedy or additional technology in an evolutionary process, it is not very efficient. In this paper, a normal vector projection method for image segmentation using Chan-Vese model is proposed. An equivalent formulation of Chan-Vese model is used by taking advantage of property of binary level set functions and combining with the concept of convex relaxation. Threshold method and projection formula are applied in the implementation. It can avoid the above problems and obtain a global optimal solution. Experimental results on both synthetic and real images validate the effects of the proposed normal vector projection method, and show advantages over traditional algorithms in terms of computational efficiency.
A Line-Search-Based Partial Proximal Alternating Directions Method for Separable Convex Optimization
Directory of Open Access Journals (Sweden)
Yu-hua Zeng
2014-01-01
Full Text Available We propose an appealing line-search-based partial proximal alternating directions (LSPPAD method for solving a class of separable convex optimization problems. These problems under consideration are common in practice. The proposed method solves two subproblems at each iteration: one is solved by a proximal point method, while the proximal term is absent from the other. Both subproblems admit inexact solutions. A line search technique is used to guarantee the convergence. The convergence of the LSPPAD method is established under some suitable conditions. The advantage of the proposed method is that it provides the tractability of the subproblem in which the proximal term is absent. Numerical tests show that the LSPPAD method has better performance compared with the existing alternating projection based prediction-correction (APBPC method if both are employed to solve the described problem.
Simulation of stochastic systems via polynomial chaos expansions and convex optimization
Fagiano, Lorenzo
2012-01-01
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a novel computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allow to take into account the specific features of Polynomial Chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated i...
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Jafarizadeh, M A; Aali, M
2009-01-01
Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success prob...
The optimal solution of a non-convex state-dependent LQR problem and its applications.
Directory of Open Access Journals (Sweden)
Xudan Xu
Full Text Available This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.
Energy Technology Data Exchange (ETDEWEB)
Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States); Chen, Ken Chung [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China); Shen, Steve G. F.; Yan, Jin [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People' s Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Lee, Philip K. M.; Chow, Ben [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China); Liu, Nancy X. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China); Xia, James J. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States); Department of Surgery (Oral and Maxillofacial Surgery), Weill Medical College, Cornell University, New York, New York 10065 (United States); Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People' s Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Shen, Dinggang, E-mail: dgshen@med.unc.edu [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)
2014-04-15
Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT
High-Dimensional Analysis of Convex Optimization-Based Massive MIMO Decoders
Ben Atitallah, Ismail
2017-04-01
A wide range of modern large-scale systems relies on recovering a signal from noisy linear measurements. In many applications, the useful signal has inherent properties, such as sparsity, low-rankness, or boundedness, and making use of these properties and structures allow a more efficient recovery. Hence, a significant amount of work has been dedicated to developing and analyzing algorithms that can take advantage of the signal structure. Especially, since the advent of Compressed Sensing (CS) there has been significant progress towards this direction. Generally speaking, the signal structure can be harnessed by solving an appropriate regularized or constrained M-estimator. In modern Multi-input Multi-output (MIMO) communication systems, all transmitted signals are drawn from finite constellations and are thus bounded. Besides, most recent modulation schemes such as Generalized Space Shift Keying (GSSK) or Generalized Spatial Modulation (GSM) yield signals that are inherently sparse. In the recovery procedure, boundedness and sparsity can be promoted by using the ℓ1 norm regularization and by imposing an ℓ∞ norm constraint respectively. In this thesis, we propose novel optimization algorithms to recover certain classes of structured signals with emphasis on MIMO communication systems. The exact analysis permits a clear characterization of how well these systems perform. Also, it allows an automatic tuning of the parameters. In each context, we define the appropriate performance metrics and we analyze them exactly in the High Dimentional Regime (HDR). The framework we use for the analysis is based on Gaussian process inequalities; in particular, on a new strong and tight version of a classical comparison inequality (due to Gordon, 1988) in the presence of additional convexity assumptions. The new framework that emerged from this inequality is coined as Convex Gaussian Min-max Theorem (CGMT).
Chen, Shibing; Wang, Xu-Jia
2016-01-01
In this paper we prove the strict c-convexity and the C 1, α regularity for potential functions in optimal transportation under condition (A3w). These results were obtained by Caffarelli [1,3,4] for the cost c (x, y) =| x - y | 2, by Liu [11], Loeper [15], Trudinger and Wang [20] for costs satisfying the condition (A3). For costs satisfying the condition (A3w), the results have also been proved by Figalli, Kim, and McCann [6], assuming that the initial and target domains are uniformly c-convex, see also [21]; and by Guillen and Kitagawa [8], assuming the cost function satisfies A3w in larger domains. In this paper we prove the strict c-convexity and the C 1, α regularity assuming either the support of source density is compactly contained in a larger domain where the cost function satisfies A3w, or the dimension 2 ≤ n ≤ 4.
Poker, Gilad; Zarai, Yoram; Margaliot, Michael; Tuller, Tamir
2014-11-06
Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation-elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.
Nedjar, Sebastien; Cicchetti, Rosine; Lakhal, Lotfi; 10.3166/isi.11.6.11-31
2010-01-01
In various approaches, data cubes are pre-computed in order to answer efficiently OLAP queries. The notion of data cube has been declined in various ways: iceberg cubes, range cubes or differential cubes. In this paper, we introduce the concept of convex cube which captures all the tuples of a datacube satisfying a constraint combination. It can be represented in a very compact way in order to optimize both computation time and required storage space. The convex cube is not an additional structure appended to the list of cube variants but we propose it as a unifying structure that we use to characterize, in a simple, sound and homogeneous way, the other quoted types of cubes. Finally, we introduce the concept of emerging cube which captures the significant trend inversions. characterizations.
Efficient convex optimization approach to 3D non-rigid MR-TRUS registration.
Sun, Yue; Yuan, Jing; Rajchl, Martin; Qiu, Wu; Romagnoli, Cesare; Fenster, Aaron
2013-01-01
In this study, we propose an efficient non-rigid MR-TRUS deformable registration method to improve the accuracy of targeting suspicious locations during a 3D ultrasound (US) guided prostate biopsy. The proposed deformable registration approach employs the multi-channel modality independent neighbourhood descriptor (MIND) as the local similarity feature across the two modalities of MR and TRUS, and a novel and efficient duality-based convex optimization based algorithmic scheme is introduced to extract the deformations which align the two MIND descriptors. The registration accuracy was evaluated using 10 patient images by measuring the TRE of manually identified corresponding intrinsic fiducials in the whole gland and peripheral zone, and performance metrics (DSC, MAD and MAXD) for the apex, mid-gland and base of the prostate were also calculated by comparing two manually segmented prostate surfaces in the registered 3D MR and TRUS images. Experimental results show that the proposed method yielded an overall mean TRE of 1.74 mm, which is favorably comparable to a clinical requirement for an error of less than 2.5 mm.
Footstep Planning on Uneven Terrain with Mixed-Integer Convex Optimization
2014-08-01
variables to absorb any non-convex constraints. We handle orientation of the footstep placements by approximating the trigonometric sin and cos...must enforce that sj and cj approximate sin and cos without introducing non-convex trigonometric constraints. We choose instead to create a simple...goal and identical cost weights on the displacement from each footstep to the next. To control the number of footsteps used in the plan, and thus the
DEFF Research Database (Denmark)
Stolpe, Mathias
2007-01-01
We consider equivalent reformulations of nonlinear mixed 0–1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. We show that the considered problems can equivalently be cast as either...... linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...
DEFF Research Database (Denmark)
Stolpe, Mathias
2004-01-01
We consider equivalent reformulations of nonlinear mixed 0-1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. It is shown that the considered problems may equivalently be cast as either...... linear or as convex quadratic mixed 0-1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...
Institute of Scientific and Technical Information of China (English)
田朝薇; 宋海洲
2011-01-01
针对非凸二次约束二次规划(QCQP)问题,将问题中二次函数的凸函数部分保留,达到所得松弛规划的可行域更加紧致的目的,得到原问题更好的下界.利用正交变换的方法得到原问题的一个凸规划松弛模型,再利用分支定界算法求其全局最优解.根据问题的最优性和可行性原则,提出一种能整体删除或缩小算法迭代过程中产生的分割子区域的区域删减策略.数值算例表明,算法及区域删减策略均是有效的.%In this paper, we obtain a sharper low bound by reserving the part of the convex function of the quadratic function for a non-convex quadratic programming with non-convex quadratic constraints (QCQP). The QCQP problem is first transformed into a convex quadratic programming with linear constraints by employing the orthogonal transformation and then the latter is solved by the branch-bound method. In order to improve the convergence of the proposed algorithm, two region-prunning techniques are given to delete or contract the sub-regions in which does not contain the optimal solutions of QCQP according to the optimality and feasibility of the problem. The numerical results show that the proposed algorithm and the prunning techniques are effective.
Directory of Open Access Journals (Sweden)
Zuliang Lu
2014-01-01
Full Text Available The aim of this work is to investigate the discretization of general linear hyperbolic convex optimal control problems by using the mixed finite element methods. The state and costate are approximated by the k order (k≥0 Raviart-Thomas mixed finite elements and the control is approximated by piecewise polynomials of order k. By applying the elliptic projection operators and Gronwall’s lemma, we derive a priori error estimates of optimal order for both the coupled state and the control approximation.
Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis
Zhang, Han; Chen, Xuefeng; Du, Zhaohui; Yan, Ruqiang
2016-12-01
The bearing failure, generating harmful vibrations, is one of the most frequent reasons for machine breakdowns. Thus, performing bearing fault diagnosis is an essential procedure to improve the reliability of the mechanical system and reduce its operating expenses. Most of the previous studies focused on rolling bearing fault diagnosis could be categorized into two main families, kurtosis-based filter method and wavelet-based shrinkage method. Although tremendous progresses have been made, their effectiveness suffers from three potential drawbacks: firstly, fault information is often decomposed into proximal frequency bands and results in impulsive feature frequency band splitting (IFFBS) phenomenon, which significantly degrades the performance of capturing the optimal information band; secondly, noise energy spreads throughout all frequency bins and contaminates fault information in the information band, especially under the heavy noisy circumstance; thirdly, wavelet coefficients are shrunk equally to satisfy the sparsity constraints and most of the feature information energy are thus eliminated unreasonably. Therefore, exploiting two pieces of prior information (i.e., one is that the coefficient sequences of fault information in the wavelet basis is sparse, and the other is that the kurtosis of the envelope spectrum could evaluate accurately the information capacity of rolling bearing faults), a novel weighted sparse model and its corresponding framework for bearing fault diagnosis is proposed in this paper, coined KurWSD. KurWSD formulates the prior information into weighted sparse regularization terms and then obtains a nonsmooth convex optimization problem. The alternating direction method of multipliers (ADMM) is sequentially employed to solve this problem and the fault information is extracted through the estimated wavelet coefficients. Compared with state-of-the-art methods, KurWSD overcomes the three drawbacks and utilizes the advantages of both family
DEFF Research Database (Denmark)
M. Gaspar, Raquel; Murgoci, Agatha
2010-01-01
of particular importance to practitioners: yield convexity adjustments, forward versus futures convexity adjustments, timing and quanto convexity adjustments. We claim that the appropriate way to look into any of these adjustments is as a side effect of a measure change, as proposed by Pelsser (2003...
Huang, Wenxuan; Dacek, Stephen; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-01-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics, among others. However, the problem of finding the true global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved, with only a limited number of results for highly simplified systems known. In this article, we present the first general algorithm to find the exact ground states of complex lattice models and to prove their global optimality, resolving this fundamental problem in condensed matter and materials theory. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and non-smooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy respectively. By systematically converging th...
Minimax-optimal rates for sparse additive models over kernel classes via convex programming
Raskutti, Garvesh; Yu, Bin
2010-01-01
Sparse additive models are families of $d$-variate functions that have the additive decomposition \\mbox{$f^* = \\sum_{j \\in S} f^*_j$,} where $S$ is a unknown subset of cardinality $s \\ll d$. We consider the case where each component function $f^*_j$ lies in a reproducing kernel Hilbert space, and analyze a simple kernel-based convex program for estimating the unknown function $f^*$. Working within a high-dimensional framework that allows both the dimension $d$ and sparsity $s$ to scale, we derive convergence rates in the $L^2(\\mathbb{P})$ and $L^2(\\mathbb{P}_n)$ norms. These rates consist of two terms: a \\emph{subset selection term} of the order $\\frac{s \\log d}{n}$, corresponding to the difficulty of finding the unknown $s$-sized subset, and an \\emph{estimation error} term of the order $s \\, \
Some Characterizations of Total Duality for a Composed Convex Optimization%复合凸优化问题全对偶性的等价刻画
Institute of Scientific and Technical Information of China (English)
孙祥凯
2015-01-01
We first introduced the dual schemes for a composed convex optimization problem.Then, using the properties of subdifferential, we introduced a new Moreau-Rockafellar formula for a composed convex function.And using the Moreau-Rockafellar formula,we obtained some necessary and sufficient conditions which characterize the stable total duality for the composed convex optimization problem.%先建立一类复合凸优化问题的对偶问题，再利用次微分性质引入关于复合凸函数的一类新的 Moreau-Rockafellar 法则，等价刻画了该复合凸优化问题的稳定全对偶及全对偶。
Continuity of Convex Set-valued Maps and a Fundamental Duality Formula for Set-valued Optimization
Heyde, Frank
2011-01-01
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays an important role. For set-valued maps different notions of continuity exist. We will compare the most prevalent ones in the special case that the image space is the set of upper closed subsets of a preordered topological vector space and analyze which of the results can be conveyed from the extended real-valued case. Moreover, we present a fundamental duality formula for set-valued optimization, using the weakest of the continuity concepts under consideration for a regularity condition.
Quoc, Tran Dinh; Diehl, Moritz
2011-01-01
A new algorithm for solving large-scale separable convex optimization problems is proposed. The basic idea is to combine three techniques including Lagrangian dual decomposition, excessive gap and smoothing techniques. The main advantage of this algorithm is to dynamically update the smoothness parameters which leads to a numerically stable performance ability. The convergence of the algorithm is proved under weak conditions imposed on the original problem. The worst-case complexity is estimated which is $O(1/k)$, where $k$ is the iteration counter. Then, the algorithm is coupled with a dual scheme to construct a switching variant of the dual decomposition. Discussion on the implementation issues is presented and theoretical comparison is analyzed. Numerical results are implemented to confirm the theoretical development.
Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.
Hoffmann, A.L.; Siem, A.Y.; Hertog, D. den; Kaanders, J.H.A.M.; Huizenga, H.
2006-01-01
In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be co
Setting Optimal Bounds on Risk in Asset Allocation - a Convex Program
Directory of Open Access Journals (Sweden)
James E. Falk
2002-10-01
Full Text Available The 'Portfolio Selection Problem' is traditionally viewed as selecting a mix of investment opportunities that maximizes the expected return subject to a bound on risk. However, in reality, portfolios are made up of a few 'asset classes' that consist of similar opportunities. The asset classes are managed by individual `sub-managers', under guidelines set by an overall portfolio manager. Once a benchmark (the `strategic' allocation has been set, an overall manager may choose to allow the sub-managers some latitude in which opportunities make up the classes. He may choose some overall bound on risk (as measured by the variance and wish to set bounds that constrain the submanagers. Mathematically we show that the problem is equivalent to finding a hyper-rectangle of maximal volume within an ellipsoid. It is a convex program, albeit with potentially a large number of constraints. We suggest a cutting plane algorithm to solve the problem and include computational results on a set of randomly generated problems as well as a real-world problem taken from the literature.
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
Negahban, Sahand
2010-01-01
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with high probability, it satisfies a form of restricted strong convexity with respect to weighted Frobenius norm. Using this property, we obtain as corollaries a number of error bounds on matrix completion in the weighted Frobenius norm under noisy sampling and for both exact and near low-rank matrices. Our results are based on measures of the "spikiness" and "low-rankness" of matrices that are less restrictive than the incoherence conditions imposed in previous work. Our technique involves an $M$-estimator that includes controls on both the rank and spikiness of the solution, and we establish non-asymptotic error bounds in weighted Frobenius norm for recovering matrices lying with $\\ell_q$-"balls" of bounded spikiness. Using information-theoretic methods, we show that no algo...
Gorissen, B.L.; Ben-Tal, A.; Blanc, J.P.C.; den Hertog, D.
2012-01-01
Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the
Convex Geometry and Stoichiometry
Jer-Chin,
2011-01-01
We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.
Huang, Wenxuan; Kitchaev, Daniil A.; Dacek, Stephen T.; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-10-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.
Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron
2014-04-01
We propose a novel global optimization-based approach to segmentation of 3-D prostate transrectal ultrasound (TRUS) and T2 weighted magnetic resonance (MR) images, enforcing inherent axial symmetry of prostate shapes to simultaneously adjust a series of 2-D slice-wise segmentations in a "global" 3-D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coherent continuous max-flow model (CCMFM), which derives a new and efficient duality-based algorithm, leading to a GPU-based implementation to achieve high computational speeds. Experiments with 25 3-D TRUS images and 30 3-D T2w MR images from our dataset, and 50 3-D T2w MR images from a public dataset, demonstrate that the proposed approach can segment a 3-D prostate TRUS/MR image within 5-6 s including 4-5 s for initialization, yielding a mean Dice similarity coefficient of 93.2%±2.0% for 3-D TRUS images and 88.5%±3.5% for 3-D MR images. The proposed method also yields relatively low intra- and inter-observer variability introduced by user manual initialization, suggesting a high reproducibility, independent of observers.
Faggian, Silvia
2007-01-01
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author, or by Faggian and Gozzi. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.
Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; McLeod, Jonathan; Chen, Yimin; de Ribaupierre, Sandrine; Fenster, Aaron
2015-02-01
A three-dimensional (3-D) ultrasound (US) system has been developed to monitor the intracranial ventricular system of preterm neonates with intraventricular hemorrhage (IVH) and the resultant dilation of the ventricles (ventriculomegaly). To measure ventricular volume from 3-D US images, a semi-automatic convex optimization-based approach is proposed for segmentation of the cerebral ventricular system in preterm neonates with IVH from 3-D US images. The proposed semi-automatic segmentation method makes use of the convex optimization technique supervised by user-initialized information. Experiments using 58 patient 3-D US images reveal that our proposed approach yielded a mean Dice similarity coefficient of 78.2% compared with the surfaces that were manually contoured, suggesting good agreement between these two segmentations. Additional metrics, the mean absolute distance of 0.65 mm and the maximum absolute distance of 3.2 mm, indicated small distance errors for a voxel spacing of 0.22 × 0.22 × 0.22 mm(3). The Pearson correlation coefficient (r = 0.97, p < 0.001) indicated a significant correlation of algorithm-generated ventricular system volume (VSV) with the manually generated VSV. The calculated minimal detectable difference in ventricular volume change indicated that the proposed segmentation approach with 3-D US images is capable of detecting a VSV difference of 6.5 cm(3) with 95% confidence, suggesting that this approach might be used for monitoring IVH patients' ventricular changes using 3-D US imaging. The mean segmentation times of the graphics processing unit (GPU)- and central processing unit-implemented algorithms were 50 ± 2 and 205 ± 5 s for one 3-D US image, respectively, in addition to 120 ± 10 s for initialization, less than the approximately 35 min required by manual segmentation. In addition, repeatability experiments indicated that the intra-observer variability ranges from 6.5% to 7.5%, and the inter-observer variability is 8.5% in terms
On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2016-01-01
In this talk we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective ...
On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2016-01-01
In this talk we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective ...
Chang, J.; Nakshatrala, K.
2014-12-01
It is well know that the standard finite element methods, in general, do not satisfy element-wise mass/species balance properties. It is, however, desirable to have element-wide mass balance property in subsurface modeling. Several studies over the years have aimed to overcome this drawback of finite element formulations. Currently, a post-processing optimization-based methodology is commonly employed to recover the local mass balance for porous media models. However, such a post-processing technique does not respect the underlying variational structure that the finite element formulation may enjoy. Motivated by this, a consistent methodology to satisfy element-wise local mass balance for porous media models is constructed using convex optimization techniques. The assembled system of global equations is reconstructed into a quadratic programming problem subjected to bounded equality constraints that ensure conservation at the element level. The proposed methodology can be applied to any computational mesh and to any non-locally conservative nodal-based finite element method. Herein, we integrate our proposed methodology into the framework of the classical mixed Galerkin formulation using Taylor-Hood elements and the least-squares finite element formulation. Our numerical studies will include computational cost, numerical convergence, and comparision with popular methods. In particular, it will be shown that the accuracy of the solutions is comparable with that of several popular locally conservative finite element formulations like the lowest order Raviart-Thomas formulation. We believe the proposed optimization-based approach is a viable approach to preserve local mass balance on general computational grids and is amenable for large-scale parallel implementation.
Nonuniqueness versus Uniqueness of Optimal Policies in Convex Discounted Markov Decision Processes
Directory of Open Access Journals (Sweden)
Raúl Montes-de-Oca
2013-01-01
Full Text Available From the classical point of view, it is important to determine if in a Markov decision process (MDP, besides their existence, the uniqueness of the optimal policies is guaranteed. It is well known that uniqueness does not always hold in optimization problems (for instance, in linear programming. On the other hand, in such problems it is possible for a slight perturbation of the functional cost to restore the uniqueness. In this paper, it is proved that the value functions of an MDP and its cost perturbed version stay close, under adequate conditions, which in some sense is a priority. We are interested in the stability of Markov decision processes with respect to the perturbations of the cost-as-you-go function.
Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt
2013-01-01
;1. lx is maintained between 1.47 and 1.70 mm from 25 mm to 70 mm and is increased to 2.8 mm at a depth of 100 mm. Parabolic profiles are estimated using 16 missions. The optimization gives a reduction in std. from 8.5% to 5.9% with a reduction in bias from 35% to 1.02% at 90 degrees (transverse flow...
Institute of Scientific and Technical Information of China (English)
胡清洁; 肖运海; 陈内萍
2009-01-01
In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288(2003) 365-382].
Institute of Scientific and Technical Information of China (English)
王彩玲; 刘庆怀; 李忠范
2008-01-01
In this paper, we introduce generalized essentially pseudoconvex func-tion and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution.We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.
Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui
2014-09-01
Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results.
Cheung, Ngaam J; Shen, Hong-Bin
2014-11-01
The stable conformation of a molecule is greatly important to uncover the secret of its properties and functions. Generally, the conformation of a molecule will be the most stable when it is of the minimum potential energy. Accordingly, the determination of the conformation can be solved in the optimization framework. It is, however, not an easy task to achieve the only conformation with the lowest energy among all the potential ones because of the high complexity of the energy landscape and the exponential computation increasing with molecular size. In this paper, we develop a hierarchical and heterogeneous particle swarm optimizer (HHPSO) to deal with the problem in the minimization of the potential energy. The proposed method is evaluated over a scalable simplified molecular potential energy function with up to 200 degrees of freedom and a realistic energy function of pseudo-ethane molecule. The experimental results are compared with other six PSO variants and four genetic algorithms. The results show HHPSO is significantly better than the compared PSOs with p-value less than 0.01277 over molecular potential energy function.
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Jørgensen, John Bagterp
2012-01-01
from the wind farm model, enabling us to use a very simple linear relationship for describing the turbine interactions. In addition, we allow individual turbines to be turned on or off introducing integer variables into the optimization problem. We solve this within the same framework of iterative...... is far superior to, a more naive distribution scheme. We employ a fast convex quadratic programming solver to carry out the iterations in the range of microseconds for even large wind farms....
基于凸包的视锥体裁剪精度优化%Precision Optimeization of View Frustum Culling Based on Convex Hull
Institute of Scientific and Technical Information of China (English)
曾磊夫; 刘爽
2016-01-01
According to the space object frustum clipping ,a kind of precision optimization method has been put forward that is based on the convex hull .First of all ,the method get the 2d plane projection from 3d object ,and organize projective coordinate to a convex hull ,finally get the visibility of objects according to the line form the coordinate of convex hull and the camera ,whole optimization needs any extra memory to save the data of convex hull only .The experimental results show that this method implement simply ,it can reduce the unreasonable result from the sphere detection or cylinder detection ,improving the whole efficiency of 3D rendering system .%针对视锥体对空间中物体的裁剪 ,提出一种新的基于凸包的精度优化方法 ,该方法首先得到三维物体到二维平面的投影 ,然后对投影坐标进行凸包组织 ,最后根据凸包上的坐标点和摄像机的连线得到物体的可见性 ,整个优化法只需一些额外的存储空间来存储物体的凸包信息即可 .实验结果表明 ,该方法易于实现 ,能减少通常的包围球、圆柱体检测法中出现的不合理结果 ,进而提高整个三维渲染系统的效率 .
Covering Numbers for Convex Functions
Guntuboyina, Adityanand
2012-01-01
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\\epsilon$-covering number of $\\C([a, b]^d, B)$, in the $L_p$-metric, $1 \\le p 0$, and $\\C([a,b]^d, B)$ denotes the set of all convex functions on $[a, b]^d$ that are uniformly bounded by $B$. We summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results. Our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems.
Klee, Victor; Ziegler, Günter
2003-01-01
"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The or...
Dynamic Planar Convex Hull with Optimal Query Time and O(log n · log log n ) Update Time
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Jakob, Riko
2000-01-01
The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time...
2012-08-01
number of practical problems can be formulated in the form of (1.1) such as convex problems: (group) Lasso [64,74] or the basis pursuit ( denoising ) [15...K) ) ) 1 ν ≤ CN− 1−θ 2θ−1 , for sufficiently large C and N . This completes the proof. 21 REFERENCES [1] M. Aharon, M. Elad, and A. Bruckstein, K- SVD
Directory of Open Access Journals (Sweden)
Insub Choi
2016-12-01
Full Text Available Existing vision-based displacement sensors (VDSs extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called “TVDS” is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS. The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.
Choi, Insub; Kim, JunHee; Kim, Donghyun
2016-12-08
Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called "TVDS") is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Directory of Open Access Journals (Sweden)
Luís F. P. Silva
2014-01-01
Full Text Available A convex condition in terms of linear matrix inequalities (LMIs is developed for the synthesis of stabilizing fuzzy state feedback controllers for nonlinear discrete-time systems with time-varying delays. A Takagi-Sugeno (T-S fuzzy model is used to represent exactly the nonlinear system in a restricted domain of the state space, called region of validity. The proposed stabilization condition is based on a Lyapunov-Krasovskii (L-K function and it takes into account the region of validity to determine a set of initial conditions for which the actual closed-loop system trajectories are asymptotically stable and do not evolve outside the region of validity. This set of allowable initial conditions is determined from the level set associated to a fuzzy L-K function as a Cartesian product of two subsets: one characterizing the set of states at the initial instant and another for the delayed state sequence necessary to characterize the initial conditions. Finally, we propose a convex programming problem to design a fuzzy controller that maximizes the set of initial conditions taking into account the shape of the region of validity of the T-S fuzzy model. Numerical simulations are given to illustrate this proposal.
Institute of Scientific and Technical Information of China (English)
张忠武; 周宇; 孟祥华; 肖永
2015-01-01
First improve the Quadrilateral method fast convex hull algorithm to adapt it to the Pyramid convex hull algorithm, and then put forward the Initial approximate convex hull algorithm.Next to the working principle of the Initial approximate convex hull algorithm is expounded, and the concrete steps of implementing description.At last, through a large number of Experimental data to analyze the acceleration of the approximate convex hull efficiency and coarse convex hull the best choice of the number of edges.%首先改进四边形法快速凸壳算法使其适应金字塔凸壳算法,进而提出初始近似凸壳算法.其次对初始近似凸壳算法的工作原理进行阐述,并其具体的实现步骤描述.最后通过大量实验数据分析近似凸壳的加速效率以及粗凸壳边数的最佳选择方案.
A convex optimization approach for path tracking of robot manipulators%基于凸规划的机械臂轨迹规划方法
Institute of Scientific and Technical Information of China (English)
赵建军; 魏毅; 朱登明; 夏时洪; 王兆其
2014-01-01
The problem of fast solving a robot manipulator’s path tracking with time constraints was studied, and a novel path tracking approach based on convex optimization was presented. To overcome the difficulties in dealing with the strong nonlinear dynamic constraints and time constraints in path tracking, the presented approach converts the nonlinear constraints into linear constraints by replacement of variables, and then adds new constraints to convert the original non convex optimization problem into a convex optimization problem, furthermore, converts it into a second order cone program (SOCP), and uses the optimization tools such as the SeDuMi to conduct the real time solving. This approach has several advantages. Firstly, SOCP problems can be solved in polynomial time by the interior point methods. Secondly, the convex optimization is globally stable and the solution is globally optimal. Besides, there is no need to provide initial values for the optimization. Thirdly, this approach has great flexibility and can be applied to the more complicated circumstances where some other types of constraints and objective functions can be taken into account, such as acceleration constraints, minimum energy objective function and minimum jerk objective function. The simulations on a six degrees of freedom robot manipulator show the better efficiency and effectiveness of the proposed approach.%研究了快速求解具有时间约束的机械臂轨迹规划问题，提出了一种基于凸规划的轨迹规划方法。该方法针对机械臂轨迹规划中动力学约束非线性强、时间约束不易处理的问题，首先通过变量替换，将非线性约束转化为线性约束，然后添加新的约束，将原始非凸优化问题转化为凸规划问题，在此基础上，将其写作二阶锥规划（SOCP）形式，使用SeDuMi等优化工具包近似实时求解。该方法具有以下优点：计算高效，凸规划问题能够在多项式时间内得到
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...
Multi-class DTI Segmentation: A Convex Approach.
Xie, Yuchen; Chen, Ting; Ho, Jeffrey; Vemuri, Baba C
2012-10-01
In this paper, we propose a novel variational framework for multi-class DTI segmentation based on global convex optimization. The existing variational approaches to the DTI segmentation problem have mainly used gradient-descent type optimization techniques which are slow in convergence and sensitive to the initialization. This paper on the other hand provides a new perspective on the often difficult optimization problem in DTI segmentation by providing a reasonably tight convex approximation (relaxation) of the original problem, and the relaxed convex problem can then be efficiently solved using various methods such as primal-dual type algorithms. To the best of our knowledge, such a DTI segmentation technique has never been reported in literature. We also show that a variety of tensor metrics (similarity measures) can be easily incorporated in the proposed framework. Experimental results on both synthetic and real diffusion tensor images clearly demonstrate the advantages of our method in terms of segmentation accuracy and robustness. In particular, when compared with existing state-of-the-art methods, our results demonstrate convincingly the importance as well as the benefit of using more refined and elaborated optimization method in diffusion tensor MR image segmentation.
Uniformly convex and strictly convex Orlicz spaces
Masta, Al Azhary
2016-02-01
In this paper we define the new norm of Orlicz spaces on ℝn through a multiplication operator on an old Orlicz spaces. We obtain some necessary and sufficient conditions that the new norm to be a uniformly convex and strictly convex spaces.
On Quasi E-Convex Bilevel Programming Problem
Directory of Open Access Journals (Sweden)
E. A. Youness
2005-01-01
Full Text Available Bilevel programming problems involve two optimization problems where the data of the first one is implicity determined by the solution of the second. This study introduces the notions of E-convexity and quasi E-convexity in bilevel programming problems to generalize quasi convex bilevel programming problems.
Machine learning a Bayesian and optimization perspective
Theodoridis, Sergios
2015-01-01
This tutorial text gives a unifying perspective on machine learning by covering both probabilistic and deterministic approaches, which rely on optimization techniques, as well as Bayesian inference, which is based on a hierarchy of probabilistic models. The book presents the major machine learning methods as they have been developed in different disciplines, such as statistics, statistical and adaptive signal processing and computer science. Focusing on the physical reasoning behind the mathematics, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. The book builds carefully from the basic classical methods to the most recent trends, with chapters written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as shor...
Pearce, Charles
2009-01-01
Focuses on mathematical structure, and on real-world applications. This book includes developments in several optimization-related topics such as decision theory, linear programming, turnpike theory, duality theory, convex analysis, and queuing theory.
Rabinowitz, Matthew; Myers, Lance; Banjevic, Milena; Chan, Albert; Sweetkind-Singer, Joshua; Haberer, Jessica; McCann, Kelly; Wolkowicz, Roland
2006-03-01
Genotype-phenotype modeling problems are often overcomplete, or ill-posed, since the number of potential predictors-genes, proteins, mutations and their interactions-is large relative to the number of measured outcomes. Such datasets can still be used to train sparse parameter models that generalize accurately, by exerting a principle similar to Occam's Razor: When many possible theories can explain the observations, the most simple is most likely to be correct. We apply this philosophy to modeling the drug response of Type-1 Human Immunodeficiency Virus (HIV-1). Owing to the decreasing expense of genetic sequencing relative to in vitro phenotype testing, a statistical model that reliably predicts viral drug response from genetic data is an important tool in the selection of antiretroviral therapy (ART). The optimization techniques described will have application to many genotype-phenotype modeling problems for the purpose of enhancing clinical decisions. We describe two regression techniques for predicting viral phenotype in response to ART from genetic sequence data. Both techniques employ convex optimization for the continuous subset selection of a sparse set of model parameters. The first technique, the least absolute shrinkage and selection operator, uses the l(1) norm loss function to create a sparse linear model; the second, the support vector machine with radial basis kernel functions, uses the epsilon-insensitive loss function to create a sparse non-linear model. The techniques are applied to predict the response of the HIV-1 virus to 10 reverse transcriptase inhibitor and 7 protease inhibitor drugs. The genetic data are derived from the HIV coding sequences for the reverse transcriptase and protease enzymes. When tested by cross-validation with actual laboratory measurements, these models predict drug response phenotype more accurately than models previously discussed in the literature, and other canonical techniques described here. Key features of the
Optimal management of genital herpes: current perspectives
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Sauerbrei A
2016-06-01
Full Text Available Andreas Sauerbrei Institute of Virology and Antiviral Therapy, German Consulting Laboratory for Herpes Simplex Virus and Varicella-Zoster Virus, Jena University Hospital, Friedrich-Schiller University of Jena, Jena, Germany Abstract: As one of the most common sexually transmitted diseases, genital herpes is a global medical problem with significant physical and psychological morbidity. Genital herpes is caused by herpes simplex virus type 1 or type 2 and can manifest as primary and/or recurrent infection. This manuscript provides an overview about the fundamental knowledge on the virus, its epidemiology, and infection. Furthermore, the current possibilities of antiviral therapeutic interventions and laboratory diagnosis of genital herpes as well as the present situation and perspectives for the treatment by novel antivirals and prevention of disease by vaccination are presented. Since the medical management of patients with genital herpes simplex virus infection is often unsatisfactory, this review aims at all physicians and health professionals who are involved in the care of patients with genital herpes. The information provided would help to improve the counseling of affected patients and to optimize the diagnosis, treatment, and prevention of this particular disease. Keywords: herpes simplex virus, epidemiology, infection, antiviral therapy, laboratory diagnosis, prevention
Bornological Locally Convex Cones
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Davood Ayaseh
2014-10-01
Full Text Available In this paper we define bornological and b-bornological cones and investigate their properties. We give some characterization for these cones. In the special case of locally convex topological vector space both these concepts reduce to the known concept of bornological spaces. We introduce and investigate the convex quasiuniform structures U_{tau}, U_{sigma}(P,P* and \\U_{beta}(P,P* on locally convex cone (P,U.
Uniformly Convex Metric Spaces
Kell Martin
2014-01-01
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...
van de Vel, MLJ
1993-01-01
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear si
Linearization functors on real convex sets
Velasco, Mauricio
2012-01-01
We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to efficient computation. These operations are convex analogues of Hom functors, tensor products, symmetric powers, exterior powers and general Schur functors on vector spaces and lead to novel constructions even for polyhedra.
On convexity in complex networks
Marc, Tilen
2016-01-01
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity. We analyze the expansion of convex subsets of nodes in empirical networks and also convexity of small subgraphs known as graphlets. We demonstrate that convexity is an inherent property of complex networks not present in a random graph. According to our perception of convexity, a convex network is such in which every connected subset of nodes induces a convex subgraph. Especially convex are technological networks and social collaboration graphs, whereas food webs are the only networks studied that are truly non-convex. Many other networks can be divided into a non-convex core surrounded by a convex periphery. We interpret convexity in terms of redundancy of shortest paths in a network and discuss possible applications.
A Mean Point Based Convex Hull Computation Algorithm
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Digvijay Singh
2016-11-01
Full Text Available The optimal solution of a Linear Programming problem (LPP is a basic feasible solution and all basic feasible solutions are extreme or boundary points of a convex region formed by the constraint functions of the LPP. In fact, the feasible solution space is not always a convex set so the verification of extreme points for optimality is quite difficult. In order to cover the non-convex feasible points within a convex set, a convex hull is imagined so that the extreme or boundary points may be checked for evaluation of the optimum solution in the decision-making process. In this article a computer assisted convex hull computation algorithm using the Mean Point and Python code verified results of the designed algorithm are discussed.
DEFF Research Database (Denmark)
Jacob, Riko
We determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure...... is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull......, and the tangent queries to determine whether a given point is inside the convex hull. The space usage of the data structure is O(n). We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....
DEFF Research Database (Denmark)
Brodal, Gerth Stølfting; Jacob, Rico
2002-01-01
In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage...... of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects...... the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure....
Recovery of Sparse Probability Measures via Convex Programming
Pilanci, Mert; El Ghaoui, Laurent; Chandrasekaran, Venkat
2012-01-01
We consider the problem of cardinality penalized optimization of a convex function over the probability simplex with additional convex constraints. The classical ℓ_1 regularizer fails to promote sparsity on the probability simplex since ℓ_1 norm on the probability simplex is trivially constant. We propose a direct relaxation of the minimum cardinality problem and show that it can be efficiently solved using convex programming. As a first application we consider recovering a spa...
Exact and Approximate Sizes of Convex Datacubes
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Statistical properties of convex clustering
Tan, Kean Ming; Witten, Daniela
2015-01-01
In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of the tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimator of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to so...
Error bound results for convex inequality systems via conjugate duality
Bot, Radu Ioan
2010-01-01
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.
Introducing convex layers to the Traveling Salesman Problem
Liew, Sing
2012-01-01
In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the TSP. On the other hand, experimental data also supports the hypothesis of convex hull i.e. human relies on convex hull to search for the optimal tour for the TSP. Secondly, from the paper published by Bonabeau, Dorigo and Theraulaz, social insect behavior would be able to help in some of the optimizing problems, especially the TSP. Thus, we propose convex layers to the TSP based on the argument that, by the analogy to the social insect behavior, untrained humans' cognition should be able to help in the TSP. Lastly, we will use Tour Improvement algorithms on convex layers to search for an optimal tour for a 13-cities problem to demonstrate the idea.
Institute of Scientific and Technical Information of China (English)
胡图; 景志宏; 张磊; 张秋林
2012-01-01
Aimed at the characteristics of cognitive Ad hoc network, a corresponding network model is established and a distributed power control algorithm based on convex optimization theory is proposed. Based on the analysis of system interference, by taking the network utility maximization as the target and transmit power of cognitive user as the solution object, a general math optimized model is formulated. Under the guidance of convex optimization theory , the model is transformed into a convex optimized model by introducing auxiliary variable and substituting variables. Lagrangian dual decomposition technique is used to solve the convex optimized model and the distributed power iterative algorithm is obtained. The simulation shows that under the premise of meeting the system constraints, the use of the proposed algorithm can obtain better system performances than that of other algorithms.%针对认知Ad hoc网络的特点,构建了相应的网络模型,提出了一种基于凸优化理论的分布式功率控制算法.在分析系统内部干扰的基础上,以最大化网络效用值为目标,以认知用户的发射功率为求解对象,建立了一个通用的数学优化模型.在凸优化理论的指导下,通过引入辅助变量和变量的对数变换,将该模型转变为等价的凸优化模型,采用拉格朗日对偶法对该模型进行求解,得到了分布式的功率迭代算法.仿真实验表明:与其他算法相比,该算法在满足系统约束条件的前提下,取得更好的系统性能.
Transverse-Mode Control of VCSELs With Convex Mirror
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
We propose the transverse-mode control of vertical-cavity surface-emitting lasers (VCSELs) with a convex mirror. A possibility of improvements on single-mode output power and higher-order mode suppression is presented by optimizing a convex mirror.
Hörmander, Lars
1994-01-01
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category. At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodiffer...
Perspective texture synthesis based on improved energy optimization.
Directory of Open Access Journals (Sweden)
Syed Muhammad Arsalan Bashir
Full Text Available Perspective texture synthesis has great significance in many fields like video editing, scene capturing etc., due to its ability to read and control global feature information. In this paper, we present a novel example-based, specifically energy optimization-based algorithm, to synthesize perspective textures. Energy optimization technique is a pixel-based approach, so it's time-consuming. We improve it from two aspects with the purpose of achieving faster synthesis and high quality. Firstly, we change this pixel-based technique by replacing the pixel computation with a little patch. Secondly, we present a novel technique to accelerate searching nearest neighborhoods in energy optimization. Using k- means clustering technique to build a search tree to accelerate the search. Hence, we make use of principal component analysis (PCA technique to reduce dimensions of input vectors. The high quality results prove that our approach is feasible. Besides, our proposed algorithm needs shorter time relative to other similar methods.
Robust Utility Maximization Under Convex Portfolio Constraints
Energy Technology Data Exchange (ETDEWEB)
Matoussi, Anis, E-mail: anis.matoussi@univ-lemans.fr [Université du Maine, Risk and Insurance institut of Le Mans Laboratoire Manceau de Mathématiques (France); Mezghani, Hanen, E-mail: hanen.mezghani@lamsin.rnu.tn; Mnif, Mohamed, E-mail: mohamed.mnif@enit.rnu.tn [University of Tunis El Manar, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT (Tunisia)
2015-04-15
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.
Subset Selection by Local Convex Approximation
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik
1999-01-01
least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function...
A generalization of the convex Kakeya problem
Ahn, Heekap
2012-01-01
We consider the following geometric alignment problem: Given a set of line segments in the plane, find a convex region of smallest area that contains a translate of each input segment. This can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be turned through 360 degrees within this region. Our main result is an optimal Θ(n log n)-time algorithm for our geometric alignment problem, when the input is a set of n line segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then the optimum placement is when the midpoints of the segments coincide. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of any rotated copy of G. © 2012 Springer-Verlag Berlin Heidelberg.
SMOOTHING BY CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Yu-mei Wang
2005-01-01
In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
A generalization of the convex Kakeya problem
Ahn, Heekap
2013-09-19
Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal Θ(nlogn)-time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of every rotated copy of G. © 2013 Springer Science+Business Media New York.
Finger-knuckle-print Recognition Based on Image Sets and Convex Optimization%面向指背关节纹识别的图像集与凸壳优化算法
Institute of Scientific and Technical Information of China (English)
徐颖; 翟懿奎; 甘俊英
2014-01-01
A finger-knuckle-print (FKP)recognition algorithm based on image set and convex hull optimization model is presented in this paper.Finger-knuckle-print image sets and Local phase quantization are utilized as inputs and feature ex-traction,then convex hull model construction and optimization is adopted for finger-knuckle-print recognition.Simulation experiments show that,the proposed algorithm has achieve good performance on the public FKP database.%本文将指背关节纹作为生物特征识别对象，提出了基于图像集与凸壳优化模型的指背关节识别算法。所提算法以指背关节纹图像集作为输入，并将局部相位特征方法用于指背关节纹特征提取，进而寻求适用于指背关节纹识别的凸壳优化模型，研究凸壳模型的构建方法并对其进行优化，从而完成指背关节纹的识别。仿真实验表明，所提算法在公开的指背关节纹中，均取得了不错的识别结果。
Egalitarianism in Convex Fuzzy Games
Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.
2002-01-01
In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a f
Average Convexity in Communication Situations
Slikker, M.
1998-01-01
In this paper we study inheritance properties of average convexity in communication situations. We show that the underlying graph ensures that the graphrestricted game originating from an average convex game is average convex if and only if every subgraph associated with a component of the underlyin
Airline Maintenance Manpower Optimization from the De Novo Perspective
Liou, James J. H.; Tzeng, Gwo-Hshiung
Human resource management (HRM) is an important issue for today’s competitive airline marketing. In this paper, we discuss a multi-objective model designed from the De Novo perspective to help airlines optimize their maintenance manpower portfolio. The effectiveness of the model and solution algorithm is demonstrated in an empirical study of the optimization of the human resources needed for airline line maintenance. Both De Novo and traditional multiple objective programming (MOP) methods are analyzed. A comparison of the results with those of traditional MOP indicates that the proposed model and solution algorithm does provide better performance and an improved human resource portfolio.
Efficient Approximation of Convex Recolorings
Moran, Shlomo; Snir, Sagi
2005-01-01
A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arise in areas such as phylogenetics, linguistics, etc. eg, a perfect phylogenetic tree is one in which the states of each character induce a convex coloring of the tree. Research on perfect phylogeny is usually focused on finding a tree so t...
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
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。
Fundamentals of convex analysis duality, separation, representation, and resolution
Panik, Michael J
1993-01-01
Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and comple...
Institute of Scientific and Technical Information of China (English)
吴灏文; 迟国泰
2012-01-01
This article builds an asset-liability portfolio optimization model to control the bank interest rate risk with directional-duration and directional convexity. It carries on the idea of directional duration, which is the first order derivative of the price of assets or liabilities to interest and will not be affected by the moving interest rates for different timing. One of the contributions of this article is that it comes up with directional convexity, which is the second order derivative of the price of assets or liabilities to interest, and broadens the way of asset-liability matching. Another is the expression of directional convexity, which is ignored by current research and which clearly represents the effects of interest rate and its changes to the discounted cash flows. The last is that it solves the problem of interest rate immunization for different interest rate changes and timing through directional duration and directional convexity.%通过方向久期和方向凸度的免疫条件来控制资产配给中的利率风险,建立了银行资产负债组合优化模型.本文通过资产或负债价格对利率一阶导数受不同时段利率变动的影响而形成方向久期的思路,提出其二阶导数也受不同时段利率变动影响形成方向凸度的概念.通过资产或负债的凸度受不同时段利率变动的影响关系给出方向凸度的表达式,反映了即期利率及其变动对贴现现金流的影响,改变了现有研究忽略利率变化对凸度的影响的状况.通过方向久期和方向凸度的双重免疫建立优化模型,解决了无论利率在不同时段的变化量是否相同均可进行风险免疫问题.
Relations between Lipschitz functions and convex functions
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Zajicek, J., On the differentation of convex functions in finite and infinite dimensional spaces, Czech J. Math.,1979, 29: 340-348.[2]Hu, T. C., Klee, V. L., Larman, D. G., Optimization of globally convex functions, SIAM J. Control Optim., 1989,27: 1026-1047.[3]Cepedello Boiso, M., Approximation of Lipschitz functions by △-convex functions in Banach spaces, Israel J.Math., 1998, 106: 269-284.[4]Asplund, E., Frechet differentiability of convex functions, Acta Math., 1968, 121: 31-47.[5]Johnson, J. A., Lipschitz spaces, Pacific J. Math, 1974, 51: 177-186.[6]Stromberg, T., The operation of infimal convolution, Dissert. Math., (Rozprawy Mat.), 1996, 325: 58.[7]Kadison, R. V., Ringrose, J. R., Fundamentals of the theory of operator algebras, volume Ⅰ: Elementary Theory,Graduate Studies in Math., vol. 15, Amer. Math. Soc., 1997.[8]Phelps, R. R., Convex functions,monotone operators and differentiability, Lect. Notes in Math., vol. 1364,Springer-Verlag, 1977.[9]Lindenstrauss, J., On operators which attain their norm, Israel J. Math., 1963, 1: 139-148.[10]Press, D., Gateaux differentiable functions are somewhere Frechet differentiable, Rend. Circ. Mat. Palermo,1984, 33: 122-133.[11]Press, D., Differentiability of Lipschitz functions on Banach spaces, J. Funct. Anal., 1990, 91:312-345.[12]Lindenstrauss, J., Press, D., On Frechet differentiability of Lipschitz maps between Banach spaces, Annals of Math., 2003, 157: 257-288.[13]Press, D., Gateaux differentiable Lipschitz functions need not be Frechet differentiable on a residual set, Supplemento Rend. Circ. Mat. Palermo, Serie Ⅱ, 1982, 2: 217-222.
H2／l1混合优化问题的凸二次规划解法%Convex Quadratic Programming for Mixed H2／l1 Optimal Control
Institute of Scientific and Technical Information of China (English)
孔亚广; 吴俊; 孙优贤
2001-01-01
采用上逼近算法求解H２／l１混合优化问题。首先将其转化为有限维的凸二次规划问题，并利用Lemke互补转轴算法求解；然后逐次进行逼近。计算示例表明所得结果是正确的。%The mixed H２／l１ optimal control is dealt with. Lowerapproximation solution is used to solve it. First, it is converted into finite dimension convex quadratic programming, and solved with Lemke complementary pivoting algorithm. Then the dimension is added until the solution convergents. At last an example is given to prove this algorithm.
Institute of Scientific and Technical Information of China (English)
朱德通
2000-01-01
使用导出的广义Fenchel对偶理论,获得了带有二次凸约束的二次凸规划问题的广义对偶形式和定理及其Kuhn-Tucker条件.进一步建立了Celis-Dennis-Tapia的信赖域子问题的对偶形式和最优性条件.%Using the generalized Fenchel's duality theory,we derive generalized duality theorems and related Kuhn-Tucker conditions for the minimization of a convex quadratic with some quadratic constraints．Further,we establish the duality programming and optimality conditions of the Celis-Dennis-Tapia trust region problem.
Introducing the Adaptive Convex Enveloping
Yu, Sheng
2011-01-01
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an accurate, fast and reliable algorithm for solving convex dynamic programs with multivariate continuous states and actions, called Adaptive Convex Enveloping. This is a short introduction of the core technique created and used in my dissertation, so it is less formal, and misses some parts, such as literature review and reference, compared to a full journal paper.
Convex polytopes and quantum states
Energy Technology Data Exchange (ETDEWEB)
Wilmott, Colin; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Heinrich-Heine-Universitaet Duesseldorf (Germany)
2010-07-01
A convex polytope is defined as the convex hull of a finite non-empty set of vectors. We present a theorem of Rado (1952) which characterizes the convex hull of the collection of all permutations of a given real d-tuple in terms of the Hardy-Littlewood-Polya spectral order relation prec. We give a necessary and sufficient condition to construct a d-dimensional convex polytope which utilizes Rado's original (d-1)-dimensional characterization, and we describe how the resulting polytope may be placed in a quantum mechanical framework.
2014-10-31
constrained quadratic program can be lifted to a convex conic optimization prob- lem. We have shown that a complementarity approach can be used to find sparse...students who were partially supported by this grant have graduated from RPI or UIUC: • Lijie Bai, On convex quadratic programs with complementarity...conferences and universities. In paper [A], we show that any quadratically constrained quadratic program is equivalent to a convex optimization problem
Watkins, N. W.; Chau, Y.; Chapman, S. C.
2010-12-01
The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].
Convex Games versus Clan Games
Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.
2006-01-01
In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games.We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games.Furthermore, each monotonic
Institute of Scientific and Technical Information of China (English)
余文权; 王华奎
2014-01-01
The synthesis of transmitting beam-pattern of a uniform linear array with a desired mainlobe amplitude re-sponse is considered as a convex optimization problem in this paper. Firstly, the whole spatial zone is divided into the mainlobe zone and sidelobe zone. Then, in the mainlobe zone, the 2-norm of the difference between the desired beampattern and the designed beampattern is minimized. In the sidelobe zone, the sidelobe peak is set to be not bigger than the desired value. Finally, the convex box is used to calculate the complex weights of sensors in the uniform linear array. Some numerical simulations are provided for demonstrating the effectiveness of the proposed beampattern syn-thesis method.%将发射阵的期望主瓣幅度响应波束设计转化为凸优化问题，并利用 cvx 工具箱求解最优加权。首先，根据期望波束的主瓣范围，将空间区域分为主瓣区域和旁瓣区域，再在主瓣区域内将设计波束和期望波束之差的2-范数最小化，并将设计波束图旁瓣级控制在期望值之下。最后，利用 cvx 工具箱对该凸优化问题进行求解，获得满足要求的设计波束图。通过计算机仿真对所提波束图设计方法的有效性进行了验证。
Convex Modeling of Interactions with Strong Heredity
Haris, Asad; Witten, Daniela; Simon, Noah
2015-01-01
We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH [Radchenko and James, 2010], hierNet [Bien et al., 2013], the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set. PMID:28316461
Ways to optimize understanding health related information: the patients' perspective.
Heinrich, Carol; Karner, Karen
2011-01-01
Self-management of chronic illness is a high priority health care need of community dwelling elderly. Effective patient provider health communication related to health promotion, disease prevention, and disease management is a key intervention necessary to achieve optimal health outcomes. Little is known about the methods elderly patients actually use to help understand health related teaching by their health care providers. Focus groups were held to describe these ways from a patient's perspective. Facilitators of understanding were identified as persevere in getting questions answered, come prepared to office visit, and work to develop a good relationship with health care providers. Barriers were identified as not having questions answered lack of time with provider, hearing difficulty, and fragmented care. Copyright © 2011 Mosby, Inc. All rights reserved.
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Jørgensen, John Bagterp
2012-01-01
We consider the optimization of power set-points to a large number of wind turbines arranged within close vicinity of each other in a wind farm. The goal is to maximize the total electric power extracted from the wind, taking the wake effects that couple the individual turbines in the farm...... into account. For any mean wind speed, turbulence intensity, and direction we find the optimal static operating points for the wind farm. We propose an iterative optimization scheme to achieve this goal. When the complicated, nonlinear, dynamics of the aerodynamics in the turbines and of the fluid dynamics...... describing the turbulent wind fields’ propagation through the farm are included in a highly detailed black-box model, numerical results for any given values of the parameter sets can easily be evaluated. However, analytic expressions for model representation in the optimization algorithms might be hard...
A novel neural network for nonlinear convex programming.
Gao, Xing-Bao
2004-05-01
In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
The Projection Neural Network for Solving Convex Nonlinear Programming
Yang, Yongqing; Xu, Xianyun
In this paper, a projection neural network for solving convex optimization is investigated. Using Lyapunov stability theory and LaSalle invariance principle, the proposed network is showed to be globally stable and converge to exact optimal solution. Two examples show the effectiveness of the proposed neural network model.
On convex relaxation of graph isomorphism.
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-03-10
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving n2 equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic.
Decision Problems For Convex Languages
Brzozowski, Janusz; Xu, Zhi
2008-01-01
In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages''). We show that we can decide whether a given language L is prefix-, suffix-, factor-, or subword-convex in polynomial time if L is represented by a DFA, but that the problem is PSPACE-hard if L is represented by an NFA. In the case that a regular language is not convex, we prove tight upper bounds on the length of the shortest words demonstrating this fact, in terms of the number of states of an accepting DFA. Similar results are proved for some subclasses of convex languages: the prefix-, suffix-, factor-, and subword-closed languages, and the prefix-, suffix-, factor-, and subword-free languages.
Maximum matching by convex quadratic programming based o an adverse graph conjecture
Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
2012-01-01
In this talk, we describe a procedure for determining a maximum stable set in a graph with convex-$QP$ stability number (which is a graph whose stability number can be determined by solving a convex quadratic programming problem) unless there is a subgraph for which neither the optimal value of the convex quadratic program nor the least adjacency eigenvalue changes when the neighborhood of any vertex is deleted. Such a graph is called adverse. Assuming the trueness of the adver...
Convex quadratic programming applied to the stability number of a graph
Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
2012-01-01
We deal with graphs whose stability number can be determined by a convex quadratic program and describe algorithmic techniques for the determination of maximum stabe sets in such graphs (except there is an induced subgraph with least adjacency eigenvalue and optimal value of the convex quadratic program not changing if the neighbourhood of any vertex is deleted). Such a graph is called adverse. Assuming that every adverse graph has convex-QP stability number, an algorithm for the recognition ...
Complex Convexity of Orlicz Modular Sequence Spaces
Directory of Open Access Journals (Sweden)
Lili Chen
2016-01-01
Full Text Available The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence space lΦ,ρ, lΦ,ρ is complex midpoint locally uniformly convex. As a corollary, lΦ,ρ is also complex strictly convex.
Uniformly convex-transitive function spaces
Rambla-Barreno, Fernando; Talponen, Jarno
2009-01-01
We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banach spaces.
On Fuzzy Simplex and Fuzzy Convex Hull
Institute of Scientific and Technical Information of China (English)
Dong QIU; Wei Quan ZHANG
2011-01-01
In this paper,we discuss fuzzy simplex and fuzzy convex hull,and give several representation theorems for fuzzy simplex and fuzzy convex hull.In addition,by giving a new characterization theorem of fuzzy convex hull,we improve some known results about fuzzy convex hull.
The Convex Coordinates of the Symmedian Point
Boyd, J. N.; Raychowdhury, P. N.
2006-01-01
In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…
Convexity Adjustments for ATS Models
DEFF Research Database (Denmark)
Murgoci, Agatha; Gaspar, Raquel M.
Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a re......Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes....... As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain exact...... formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant...
Compactly convex sets in linear topological spaces
Banakh, T; Ravsky, O
2012-01-01
A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\\Phi:X\\to exp(X)$ such that $[x,y]\\subset\\Phi(x)\\cup \\Phi(y)$ for all $x,y\\in X$. We prove that each convex subset of the plane is compactly convex. On the other hand, the space $R^3$ contains a convex set that is not compactly convex. Each compactly convex subset $X$ of a linear topological space $L$ has locally compact closure $\\bar X$ which is metrizable if and only if each compact subset of $X$ is metrizable.
Institute of Scientific and Technical Information of China (English)
向宇; 陈铁军; 陈治湘
2013-01-01
Aiming at the problem of solving differential game guidance law(DGL),a convex optimization theory is introduced and the solution method of DGL is designed by converting it into the process of solving Hamilton system.Through analyzing the gradient features of the cost function,the necessary and sufficient conditions that the game system exists anchor points is derived,and the solving method of the game system is deduced too.The result of is expected to solve the problem that the usual solving methods of DGL are not able to reflect the true process of air combat by simplifying models.%针对三维微分对策制导律(DGL)求解问题,引入凸优化理论,将DGL求解归结到Hamilton系统的求解,设计了DGL求解算法,通过对代价函数梯度特征的凸分析,推导出对策系统鞍点存在的充要条件和求解方法,解决了以往通过对微分对策模型简化求解导致的模型不能客观反映作战过程的问题.
Powers of Convex-Cyclic Operators
Directory of Open Access Journals (Sweden)
Fernando León-Saavedra
2014-01-01
Full Text Available A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex-cyclic operators. We provide an example of a convex-cyclic operator T such that the power Tn fails to be convex cyclic. Using this result we solve three questions posed by Rezaei (2013.
A class of free locally convex spaces
Sipacheva, O. V.
2003-04-01
Stratifiable spaces are a natural generalization of metrizable spaces for which Dugundji's theorem holds. It is proved that the free locally convex space of a stratifiable space is stratifiable. This means, in particular, that the space of finitely supported probability measures on a stratifiable space is a retract of a locally convex space, and that each stratifiable convex subset of a locally convex space is a retract of a locally convex space.
New Perspectives in Thermoelectric Energy Recovery System Design Optimization
Hendricks, Terry J.; Karri, Naveen K.; Hogan, Tim P.; Cauchy, Charles J.
2013-07-01
It is highly desirable to develop technologies that recover the large amounts of waste heat generated worldwide in industrial processes, automotive transportation, diesel engine exhaust, military generators, and incinerators to increase fuel efficiency and reduce CO2 production and the environmental footprint of these applications. Recent work has investigated new thermoelectric (TE) materials and systems that can operate at higher performance levels and show a viable pathway to lightweight, small-form-factor, advanced thermoelectric generator (TEG) systems to recover waste heat in many of these applications. New TE materials include nanocomposite materials such as lead-antimony-silver-telluride (LAST) and lead-antimony-silver-tin-telluride (LASTT) compounds. These new materials have created opportunities for high-performance, segmented-element TE devices. New higher-performance TE devices segmenting LAST/LASTT materials with bismuth telluride have been designed and fabricated. Sectioned TEG systems using these new TE devices and materials have been designed. Integrated heat exchanger/TE device system analyses of sectioned TE system designs have been performed, creating unique efficiency-power maps that provide better understanding and comparisons of design tradeoffs and nominal and off-nominal system performance conditions. New design perspectives and mathematical foundations in optimization of sectioned TE design approaches are discussed that provide insight on how to optimize such sectioned TE systems. System performance analyses using ANSYS® TE modeling capabilities have integrated heat exchanger performance models with ANSYS® TE models to extend its analysis capabilities beyond simple constant hot-side and cold-side temperature conditions. Analysis results portray external resistance effects, matched load conditions, and maximum power versus maximum efficiency points simultaneously, and show that maximum TE power occurs at external resistances slightly
The genealogy of convex solids
Domokos, Gabor; Szabó, Timea
2012-01-01
The shape of homogeneous, smooth convex bodies as described by the Euclidean distance from the center of gravity represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity- preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also defines a hierarchical order among convex solids and general- izes the known classification scheme in [35], ...
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.
NP-completeness of weakly convex and convex dominating set decision problems
Directory of Open Access Journals (Sweden)
Joanna Raczek
2004-01-01
Full Text Available The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \\(NP\\-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.
Institute of Scientific and Technical Information of China (English)
杨柳; 向琼; 熊瑶; 彭伶
2016-01-01
This paper is mainly considering the problem of optimal integrated production planning of the re-manufacture.We construct a joint probability constrained optimization model for this problem.As for the difficulty of the non-convex in numerical methods,we first convert the model into a convex optimization problem by using a CVaR approximation equivalently.Then a sample average approximation (SAA)method is used to solve the convex approximated model.We prove the convergence of the SAA method and numeri-cal results are given to show the effectiveness of the model and method.%研究企业再制造综合生产计划问题，构建了一个更符合实际的带联合概率约束的最优化模型。针对此非凸优化问题求解上的困难，采用 CVaR 逼近将模型等价转化为凸优化模型，然后运用样本平均近似方法进行求解，证明了算法的收敛性，数值结果表明了模型和算法的有效性。
Local Routing in Convex Subdivisions
DEFF Research Database (Denmark)
Bose, Prosenjit; Durocher, Stephane; Mondal, Debajyoti;
2015-01-01
In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted...... classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required Θ(logn) state bits to be stored and passed with the message. We present...... the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and the first local geometric memoryless routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions) when the algorithm has knowledge...
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations.......We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...... to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations....
Entanglement Quantification Made Easy: Polynomial Measures Invariant under Convex Decomposition.
Regula, Bartosz; Adesso, Gerardo
2016-02-19
Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are available in only a few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only one pure unentangled state in its range. This allows for the analytical evaluation of convex roof extended entanglement measures in classes of rank-2 states obeying such a condition. We give explicit examples for the square root of the three-tangle in three-qubit states, and we show that several representative classes of four-qubit pure states have marginals that enjoy this property.
Institute of Scientific and Technical Information of China (English)
Chuan Qiang CHEN; Bo Wen HU
2013-01-01
We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations.Under certain general structure condition,we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations.At last,we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.
Revisiting separation properties of convex fuzzy sets
Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointne...
A Note on Permutationally Convex Games
van Velzen, S.; Hamers, H.J.M.; Norde, H.W.
2005-01-01
In this paper we generalise marginal vectors and permutational convexity.We show that if a game is generalised permutationally convex, then the corresponding generalised marginal vector is a core element.Furthermore we refine the concept of permutational convexity and show that this refinement yield
On Uniform Convexity of Banach Spaces
Institute of Scientific and Technical Information of China (English)
Qing Jin CHENG; Bo WANG; Cui Ling WANG
2011-01-01
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.
Computing farthest neighbors on a convex polytope
Cheong, O.; Shin, C.S.; Vigneron, A.
2002-01-01
Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R³ into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in expecte
Computing farthest neighbors on a convex polytope
Cheong, O.; Shin, C.S.; Vigneron, A.
2002-01-01
Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R³ into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in
Generalized geometrically convex functions and inequalities.
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017-01-01
In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.
Firey linear combinations of convex bodies
Institute of Scientific and Technical Information of China (English)
XIONG Ge; XIAO Qi-ming; CHEUNG Wing-Sum
2009-01-01
For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of convex body and its polar body is given.
Bioreactor design and optimization – a future perspective
DEFF Research Database (Denmark)
Gernaey, Krist
2011-01-01
Bioreactor design and optimisation are essential in translating the experience gained from lab or pilot scale experiments to efficient production processes in industrial scale bioreactors. This article gives a future perspective on bioreactor design and optimisation, where it is foreseen...
Generalized Line Spectral Estimation via Convex Optimization
Heckel, Reinhard; Soltanolkotabi, Mahdi
2016-01-01
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we do not have access directly to such equispaced samples. Rather we only observe a severely undersampled version of these observations through linear measurements. This paper is about such generalized line spectral estimation problems. We reformulate these p...
Skala, Vaclav
2016-06-01
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.
Optimism and Pessimism in Social Context: An Interpersonal Perspective on Resilience and Risk
Smith, Timothy W.; Ruiz, John M.; Cundiff, Jenny M.; Baron, Kelly G.; Nealey-Moore, Jill B.
2016-01-01
Using the interpersonal perspective, we examined social correlates of dispositional optimism. In Study 1, optimism and pessimism were associated with warm-dominant and hostile-submissive interpersonal styles, respectively, across four samples, and had expected associations with social support and interpersonal stressors. In 300 married couples, Study 2 replicated these findings regarding interpersonal styles, using self-reports and spouse ratings. Optimism-pessimism also had significant actor and partner associations with marital quality. In Study 3 (120 couples), husbands’ and wives’ optimism predicted increases in their own marital adjustment over time, and husbands’ optimism predicted increases in wives’ marital adjustment. Thus, the interpersonal perspective is a useful integrative framework for examining social processes that could contribute to associations of optimism-pessimism with physical health and emotional adjustment. PMID:27840458
Dinh, Quoc Tran; Michiels, Wim; Diehl, Moritz
2011-01-01
A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synthesis problems are presented. In these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from COMPleib library.
A noncommutative convexity in C*-bimodules
Directory of Open Access Journals (Sweden)
Mohsen Kian
2017-02-01
Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.
Optimization strategies for discrete multi-material stiffness optimization
DEFF Research Database (Denmark)
Hvejsel, Christian Frier; Lund, Erik; Stolpe, Mathias
2011-01-01
Design of composite laminated lay-ups are formulated as discrete multi-material selection problems. The design problem can be modeled as a non-convex mixed-integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack...... larger problem instances we formulate convex and non-convex continuous relaxations which can be solved using gradient based optimization algorithms. The convex relaxation yields a lower bound on the attainable performance. The optimal solution to the convex relaxation is used as a starting guess...
Evaluating convex roof entanglement measures.
Tóth, Géza; Moroder, Tobias; Gühne, Otfried
2015-04-24
We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples.
Convex Hulls of Algebraic Sets
Gouveia, João
2010-01-01
This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of polynomials and the dual theory of moment matrices. The main feature of the technique is that all computations are done modulo the ideal generated by the polynomials defining the set to the convexified. This work was motivated by questions raised by Lov\\'asz concerning extensions of the theta body of a graph to arbitrary real algebraic varieties, and hence the relaxations described here are called theta bodies. The convexification process can be seen as an incarnation of Lasserre's hierarchy of convex relaxations of a semialgebraic set in R^n. When the defining ideal is real radical the results become especially nice. We provide several examples of the method and discuss convergence issues. Finite convergence, especially after the first step of the method, can be described expl...
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.
Barriers to optimal diabetes care in Trinidad and Tobago: a health care Professionals’ perspective
Roopnarinesingh, Nira; Brennan, Nancyellen; Khan, Claude; Ladenson, Paul W.; Hill-Briggs, Felicia; Kalyani, Rita Rastogi
2015-01-01
Background The republic of Trinidad and Tobago (T&T) is a middle income country with a comparatively high prevalence of diabetes mellitus (DM) compared to others in the Caribbean. To date, there have been no studies on health care professionals’ (HCP) perspectives regarding the barriers to achieving optimal care of patients with DM in this country and few previous studies in the Caribbean, yet such perspectives are imperative to develop strategies that reduce the global burden of this disease...
Optimal Taxation and Social Insurance in a Lifetime Perspective
DEFF Research Database (Denmark)
Bovenberg, A. Lans; Sørensen, Peter Birch
Advances in information technology have improved the administrative feasibility of redistribution based on lifetime earnings recorded at the time of retirement. We study optimal lifetime income taxation and social insurance in an economy in which redistributive taxation and social insurance serve...... to insure (ex ante) against skill heterogeneity as well as disability risk. Optimal disability benefits rise with previous earnings so that public transfers depend not only on current earnings but also on earnings in the past. Hence, lifetime taxation rather than annual taxation is optimal. The optimal tax......-transfer system does not provide full disability insurance. By offering imperfect insurance and structuring disability benefits so as to enable workers to insure against disability by working harder, social insurance is designed to offset the distortionary impact of the redistributive labor income tax on labor...
Optimal Taxation and Social Insurance in a Lifetime Perspective
DEFF Research Database (Denmark)
Bovenberg, A. Lans; Sørensen, Peter Birch
to insure (ex ante) against skill heterogeneity as well as disability risk. Optimal disability benefits rise with previous earnings so that public transfers depend not only on current earnings but also on earnings in the past. Hence, lifetime taxation rather than annual taxation is optimal. The optimal tax......Advances in information technology have improved the administrative feasibility of redistribution based on lifetime earnings recorded at the time of retirement. We study optimal lifetime income taxation and social insurance in an economy in which redistributive taxation and social insurance serve......-transfer system does not provide full disability insurance. By offering imperfect insurance and structuring disability benefits so as to enable workers to insure against disability by working harder, social insurance is designed to offset the distortionary impact of the redistributive labor income tax on labor...
Optimal Taxation and Social Insurance in a Lifetime Perspective
DEFF Research Database (Denmark)
Bovenberg, A. Lans; Sørensen, Peter Birch
Advances in information technology have improved the administrative feasibility of redistribution based on lifetime earnings recorded at the time of retirement. We study optimal lifetime income taxation and social insurance in an economy in which redistributive taxation and social insurance serve......-transfer system does not provide full disability insurance. By offering imperfect insurance and structuring disability benefits so as to enable workers to insure against disability by working harder, social insurance is designed to offset the distortionary impact of the redistributive labor income tax on labor...... to insure (ex ante) against skill heterogeneity as well as disability risk. Optimal disability benefits rise with previous earnings so that public transfers depend not only on current earnings but also on earnings in the past. Hence, lifetime taxation rather than annual taxation is optimal. The optimal tax...
Use of Convexity in Ostomy Care
Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel
2017-01-01
Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes. PMID:28002174
Perspective Application of Passive Optical Network with Optimized Bus Topology
Directory of Open Access Journals (Sweden)
P. Lafata
2012-06-01
Full Text Available Passive optical networks (PONs represent a promising solution for modern access telecommunication networks.These networks are able to meet the increasing demands on transmission rate for demanding multimedia services,while they can offer typical shared transmission speed of 1.25 or 2.5 Gbps. The major role in deploying opticaldistribution networks ODNs plays the maximum attenuable loss, which is caused mainly by passive optical splitters.This paper proposes an innovative application of passive optical networks with optimized bus topology especially forlocal backbone data networks. Due to using only passive components, it is necessary to optimize certain parameters,especially an overall attenuation balance. Considering the possibility of such optimization, the passive optical networkwith optimized bus topology provides several interesting opportunities for specific applications. This paper will presentselected aspects of passive optical networks and splitters with asymmetric splitting ratio. The essential part is focusedon the practical demonstration of their use to optimize the passive optical network with bus topology, which acts as alocal backbone network for structured cabling systems, and for local data networks in large buildings.
CONVEX CLASS OF STARLIKE FUNCTIONS
Gupta, V. P.
1984-01-01
Let ＄S＄ denote the class of functions of the form ＄f(z)=z-￥sum_{n=2}^{￥infty}|a_{n}|z^{n}＄ that are analytic and univalent in the unit disk ＄U＄. Let ＄S(￥alpha, ￥beta)＄ and ＄K(￥alpha, ￥beta)＄ denote the subclasses of ＄S＄ consisting respectively, of starlike and close-to-convex functions of order ＄￥alpha(0￥leqq￥alpha
Optimal management of urosepsis from the urological perspective.
Wagenlehner, Florian M E; Weidner, Wolfgang; Naber, Kurt G
2007-11-01
Urosepsis in adults comprises approximately 25% of all sepsis cases and in most cases is due to complicated urinary tract infections (UTIs). In this paper we review the optimal management of urosepsis from the urological point of view. Urosepsis is often due to obstructed uropathy of the upper or lower urinary tract. The treatment of urosepsis comprises four major aspects: 1. Early goal-directed therapy; 2. Optimal pharmacodynamic exposure to antimicrobials both in blood and in the urinary tract; 3. Control of complicating factors in the urinary tract; 4. Specific sepsis therapy. Early tissue oxygenation, appropriate initial antibiotic therapy and rapid identification and control of the septic focus in the urinary tract are critical steps in the successful management of a patient with severe urosepsis. To achieve this goal an optimal interdisciplinary approach encompassing the emergency unit, urological specialties and intensive-care medicine is necessary.
A New Representation and Algorithm for Constructing Convex Hulls in Higher Dimensional Spaces
Institute of Scientific and Technical Information of China (English)
吕伟; 梁友栋
1992-01-01
This paper presents a new and simple scheme to describe the convex hull in Rd,which only uses three kinds of the faces of the convex hull.i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop and efficient new algorithm for constructing the convex hull of a finite set of points incrementally.This algorithm employs much less storage and time than that of the previously-existing approaches.The analysis of the runniing time as well as the storage for the new algorithm is also theoretically made.The algorithm is optimal in the worst case for even d.
Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Balashov, Maxim V.; Repovš, Dušan,
2011-01-01
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.
Various Expressions for Modulus of Random Convexity
Institute of Scientific and Technical Information of China (English)
Xiao Lin ZENG
2013-01-01
We first prove various kinds of expressions for modulus of random convexity by using an Lo(F,R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals,then establish some basic properties including continuity for modulus of random convexity.In particular,we express the modulus of random convexity of a special random normed module Lo(F,X) derived from a normed space X by the classical modulus of convexity of X.
How to Improve Academic Optimism? an Inquiry from the Perspective of School Resource and Investment
Wu, Jason Hsinchieh; Sheu, Tian-Ming
2015-01-01
Previous studies have identified many school variables which can have significant effect on academic optimism. However, most of these identified variables are leadership or psychological constructs; thus, it is often too abstract for school administrators to translate into real practice. Therefore, this study adopted the perspective of school…
How to Improve Academic Optimism? an Inquiry from the Perspective of School Resource and Investment
Wu, Jason Hsinchieh; Sheu, Tian-Ming
2015-01-01
Previous studies have identified many school variables which can have significant effect on academic optimism. However, most of these identified variables are leadership or psychological constructs; thus, it is often too abstract for school administrators to translate into real practice. Therefore, this study adopted the perspective of school…
Eren, Altay
2012-01-01
This study aimed to examine the mediating role of prospective teachers' academic optimism in the relationship between their future time perspective and professional plans about teaching. A total of 396 prospective teachers voluntarily participated in the study. Correlation, regression, and structural equation modeling analyses were conducted in…
Optimal Taxation and Social Insurance in a Lifetime Perspective
DEFF Research Database (Denmark)
Bovenberg, A. Lans; Sørensen, Peter Birch
Advances in information technology have improved the administrative feasibility of redistribution based on lifetime earnings recorded at the time of retirement. We study optimal lifetime income taxation and social insurance in an economy in which redistributive taxation and social insurance serve...
Technology Optimism in a Socio-Economic Perspective
DEFF Research Database (Denmark)
Røpke, Inge
1996-01-01
the need for changes in fundamental mechanisms, power structures and basic ideas as preconditions for influencing the direction of technological change. The paper deals with the state interventionist version of technology optimism, where it is emphasized that active industrial and technology policies...
Institute of Scientific and Technical Information of China (English)
CHENG LIXIN; TENG YANMEI
2005-01-01
This paper presents a type of variational principles for real valued w* lower semicon tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.
A simple view on convex analysis and its applications
J. Brinkhuis (Jan); V. Tikhomirov
2005-01-01
textabstractOur aim is to give a simple view on the basics and applications of convex analysis. The essential feature of this account is the systematic use of the possibility to associate to each convex object---such as a convex set, a convex function or a convex extremal problem--- a cone, without
Entropy coherent and entropy convex measures of risk
Laeven, R.J.A.; Stadje, M.
2013-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex measur
Bot, Radu Ioan
2010-01-01
A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the qualification conditions in the context of different problem formulations in this area. We show that not only the meanwhile classical generalized interiority point ones come here to bear, but also a recently introduced one formulated by means of the quasi-relative interior.
Perspective: Codesign for materials science: An optimal learning approach
Lookman, Turab; Alexander, Francis J.; Bishop, Alan R.
2016-05-01
A key element of materials discovery and design is to learn from available data and prior knowledge to guide the next experiments or calculations in order to focus in on materials with targeted properties. We suggest that the tight coupling and feedback between experiments, theory and informatics demands a codesign approach, very reminiscent of computational codesign involving software and hardware in computer science. This requires dealing with a constrained optimization problem in which uncertainties are used to adaptively explore and exploit the predictions of a surrogate model to search the vast high dimensional space where the desired material may be found.
Efficient Line Searching for Convex Functions
den Boef, E.; den Hertog, D.
2004-01-01
In this paper we propose two new line search methods for convex functions. These new methods exploit the convexity property of the function, contrary to existing methods.The worst method is an improved version of the golden section method.For the second method it is proven that after two evaluations
Introduction to Convex and Quasiconvex Analysis
J.B.G. Frenk (Hans); G. Kassay
2004-01-01
textabstractIn the first chapter of this book the basic results within convex and quasiconvex analysis are presented. In Section 2 we consider in detail the algebraic and topological properties of convex sets within Rn together with their primal and dual representations. In Section 3 we apply the re
Stochastic Dominance: Convexity and Some Efficiency Tests
A.M. Lizyayev (Andrey)
2009-01-01
textabstractThis paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following
Convex trace functions of several variables
DEFF Research Database (Denmark)
Hansen, Frank
2002-01-01
We prove that the function (x1,...,xk)¿Tr(f(x1,...,xk)), defined on k-tuples of symmetric matrices of order (n1,...,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,...,xk) is defined by the functional calculus for functions of several variables, and it ...
1990-01-01
to Convex Bodies, Geometriae Dedicata 2" (1973) 225-248. 10. H. Guggenheimer, "The Analytic Geometry of the Unsymmetric Minkowski Plane," Lecture...Mathematics, Vol. 58, No. 2, 1975. 19. E. Lutwak, "On Cross-Sectional Measures of Polar Reciprocal Convex Bodies," Geometriae Dedicata 5, (1976) 79-80
Differential analysis of matrix convex functions II
DEFF Research Database (Denmark)
Hansen, Frank; Tomiyama, Jun
2009-01-01
We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divide...
Swanson, David
2011-01-01
We give elementary proofs of formulas for the area and perimeter of a planar convex body surrounded by a band of uniform thickness. The primary tool is a integral formula for the perimeter of a convex body which describes the perimeter in terms of the projections of the body onto lines in the plane.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
YOE ITOKAWA; KATSUHIRO SHIOHAMA; BANKTESHWAR TIWARI
2016-10-01
The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.
Toric geometry of convex quadrilaterals
Legendre, Eveline
2009-01-01
We provide an explicit resolution of the Abreu equation on convex labeled quadrilaterals. This confirms a conjecture of Donaldson in this particular case and implies a complete classification of the explicit toric K\\"ahler-Einstein and toric Sasaki-Einstein metrics constructed in [6,23,14]. As a byproduct, we obtain a wealth of extremal toric (complex) orbi-surfaces, including K\\"ahler-Einstein ones, and show that for a toric orbi-surface with 4 fixed points of the torus action, the vanishing of the Futaki invariant is a necessary and sufficient condition for the existence of K\\"ahler metric with constant scalar curvature. Our results also provide explicit examples of relative K-unstable toric orbi-surfaces that do not admit extremal metrics.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of K. Here, shape means the equivalence class of all convex bodies...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available....... The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...
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...
A Note on Upper Convex Density
Institute of Scientific and Technical Information of China (English)
YIN JIAN-DONG; ZHOU ZUO-LING
2010-01-01
For a self-similar set E satisfying the open set condition,upper convex density is an important concept for the computation of its Hausdorff measure,and it is well known that the set of relative interior points with upper convex density 1has a full Hausdorff measure.But whether the upper convex densities of E at all the relative interior points are equal to 1? In other words,whether there exists a relative interior point of E such that the upper convex density of E at this point is less than 1?In this paper,the authors construct a self-similar set satisfying the open set condition,which has a relative interior point with upper convex density less than 1.Thereby,the above problem is sufficiently answered.
Zachos, Anastasios
2010-01-01
We obtain the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and derive a plasticity principle which states that: Given four shortest arcs which meet at the weighted Fermat-Torricelli point P_F and their endpoints form a convex quadrilateral, an increase of the weight that corresponds to a shortest arc causes a decrease to the two weights that correspond to the two neighboring shortest arcs and an increase to the weight that corresponds to the opposite shortest arc. We show a connection between the plasticity of convex quadrilaterals on a complete convex surface with bounded specific curvature with the plasticity of generalized convex quadrilaterals on a manifold which is composed by triangles located on a complete convex surface of bounded specific curvature and triangles located on a two dimensional sphere whose constant Gaussian curvature equals to the infimum or supremum of the specific curvature. Furthermore, we give some cases of geometrizatio...
Institute of Scientific and Technical Information of China (English)
巩敦卫; 耿娜; 张勇
2012-01-01
密集障碍物环境下，考虑机器人移动过程中的控制偏差进行路径规划，尚缺乏有效的方法．本文的方法是：首先根据障碍物之间的最小距离和机器人尺寸的大小关系，确定凸包形成的条件；然后，通过选择满足条件的顶点，形成密集障碍物的凸包；最后，基于凸包的关键点和稀疏障碍物的位置，采用微粒群优化规划机器人路径．仿真和实验结果验证了所提方法的可行性．%Effective methods are lacking for planning robot path while considering control deviation in an environment , ： with dense obstacles. In our approach, we first determine the prerequisites for forming a convex hull according to the relation between the robot size and the minimal distance between obstacles, and then, we form the convex hull of these dense obstacles by choosing vertices that satisfy certain conditions; finally, the particle swarm optimization is applied to planning the robot path based on the positions of the key vertices in the convex hull and the positions sparse obstacles. Simulation and experiment results validate the feasibility of our method.
Constrained spacecraft reorientation using mixed integer convex programming
Tam, Margaret; Glenn Lightsey, E.
2016-10-01
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
Recognition of Graphs with Convex Quadratic Stability Number
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
PRECONDITIONED SPECTRAL PROJECTED GRADIENT METHOD ON CONVEX SETS
Institute of Scientific and Technical Information of China (English)
Lenys Bello; Marcos Raydan
2005-01-01
The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.
Convex Clustering: An Attractive Alternative to Hierarchical Clustering
Chen, Gary K.; Chi, Eric C.; Ranola, John Michael O.; Lange, Kenneth
2015-01-01
The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/ PMID:25965340
Convex integration theory solutions to the h-principle in geometry and topology
Spring, David
1998-01-01
This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, u...
The optimization of transactional emails in a marketing perspective : Incomedia case
Valieri, Simona; Marin, Nicola
2012-01-01
Aim: Optimize the usage of transactional emails, going beyond their communicative nature and combining it with marketing purposes. The project has been developed in collaboration with Incomedia, Italian software developer and vendor. Objective: Understand how Incomedia can exploit the benefits of transactional emails in a marketing perspective in order to increase the sales of its software. Limitation: The specificity of the topic, strictly related to Incomedia’s activities, products and con...
Prolonging sensor networks lifetime using convex clusters
Directory of Open Access Journals (Sweden)
Payam Salehi
2013-11-01
Full Text Available Reducing the energy consumption of nodes in sensor networks and prolonging the network life time has been proposed as one of the most important challenges facing researchers in the field of sensor networks. Therefore, designing an energy-aware protocol to gather data from network level and transmitting it to sink is placed on the agenda at this paper. After presenting an analysis of the processes of clustering in sensory networks and investigating the effect of sending interval on the amount of energy consumption, We have shown that if the use of convex static casters be done such as all the communications within the cluster with the sending distance less than the optimal threshold, it Will help to increase the lifetime of nodes. also have shown that if we create a virtual backbone between cluster heads to transfer far cluster heads data from sink to sink , will has a significant impact on increasing the network lifetime. For this reason, a detailed discussion on how to determine the size of clusters and partitioning of the network environment to them is presented in Chapter 4.Simulation results show considerable improvement of the proposed algorithm.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Convex weighting criteria for speaking rate estimation
Jiao, Yishan; Berisha, Visar; Tu, Ming; Liss, Julie
2015-01-01
Speaking rate estimation directly from the speech waveform is a long-standing problem in speech signal processing. In this paper, we pose the speaking rate estimation problem as that of estimating a temporal density function whose integral over a given interval yields the speaking rate within that interval. In contrast to many existing methods, we avoid the more difficult task of detecting individual phonemes within the speech signal and we avoid heuristics such as thresholding the temporal envelope to estimate the number of vowels. Rather, the proposed method aims to learn an optimal weighting function that can be directly applied to time-frequency features in a speech signal to yield a temporal density function. We propose two convex cost functions for learning the weighting functions and an adaptation strategy to customize the approach to a particular speaker using minimal training. The algorithms are evaluated on the TIMIT corpus, on a dysarthric speech corpus, and on the ICSI Switchboard spontaneous speech corpus. Results show that the proposed methods outperform three competing methods on both healthy and dysarthric speech. In addition, for spontaneous speech rate estimation, the result show a high correlation between the estimated speaking rate and ground truth values. PMID:26167516
Quasi-convex Functions in Carnot Groups
Institute of Scientific and Technical Information of China (English)
Mingbao SUN; Xiaoping YANG
2007-01-01
In this paper, the authors introduce the concept of h-quasiconvex functions on Carnot groups G. It is shown that the notions of h-quasiconvex functions and h-convex sets are equivalent and the L∞ estimates of first derivatives of h-quasiconvex functions are given. For a Carnot group G of step two, it is proved that h-quasiconvex functions are locally bounded from above. Furthermore, the authors obtain that h-convex functions are locally Lipschitz continuous and that an h-convex function is twice differentiable almost everywhere.
On the vertex index of convex bodies
Bezdek, Karoly
2011-01-01
We introduce the vertex index, vein(K), of a given centrally symmetric convex body K, which, in a sense, measures how well K can be inscribed into a convex polytope with small number of vertices. This index is closely connected to the illumination parameter of a body, introduced earlier by the first named author, and, thus, related to the famous conjecture in Convex Geometry about covering of a d-dimensional body by 2^d smaller positively homothetic copies. We provide asymptotically sharp estimates (up to a logarithmic term) of this index in the general case. Also, we provide sharp estimates in dimensions 2 and 3.
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
Revising incompletely specified convex probabilistic belief bases
CSIR Research Space (South Africa)
Rens, G
2016-04-01
Full Text Available International Workshop on Non-Monotonic Reasoning (NMR), 22-24 April 2016, Cape Town, South Africa Revising Incompletely Specified Convex Probabilistic Belief Bases Gavin Rens CAIR_, University of KwaZulu-Natal, School of Mathematics, Statistics...
Relations between Lipschitz functions and convex functions
Institute of Scientific and Technical Information of China (English)
RUAN Yingbin
2005-01-01
We discuss the relationship between Lipschitz functions and convex functions.By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differentiable to be residual.
Some integral inequalities for logarithmically convex functions
Directory of Open Access Journals (Sweden)
Mevlüt Tunç
2014-07-01
Full Text Available The main aim of the present note is to establish new Hadamard like integral inequalities involving log-convex function. We also prove some Hadamard-type inequalities, and applications to the special means are given.
Broom, A; Gibson, A F; Broom, J; Kirby, E; Yarwood, T; Post, J J
2016-11-01
Antibiotic optimization in hospitals is an increasingly critical priority in the context of proliferating resistance. Despite the emphasis on doctors, optimizing antibiotic use within hospitals requires an understanding of how different stakeholders, including non-prescribers, influence practice and practice change. This study was designed to understand Australian hospital managers' perspectives on antimicrobial resistance, managing antibiotic governance, and negotiating clinical vis-à-vis managerial priorities. Twenty-three managers in three hospitals participated in qualitative semi-structured interviews in Australia in 2014 and 2015. Data were systematically coded and thematically analysed. The findings demonstrate, from a managerial perspective: (1) competing demands that can hinder the prioritization of antibiotic governance; (2) ineffectiveness of audit and monitoring methods that limit rationalization for change; (3) limited clinical education and feedback to doctors; and (4) management-directed change processes are constrained by the perceived absence of a 'culture of accountability' for antimicrobial use amongst doctors. Hospital managers report considerable structural and interprofessional challenges to actualizing antibiotic optimization and governance. These challenges place optimization as a lower priority vis-à-vis other issues that management are confronted with in hospital settings, and emphasize the importance of antimicrobial stewardship (AMS) programmes that engage management in understanding and addressing the barriers to change. Copyright © 2016 The Healthcare Infection Society. Published by Elsevier Ltd. All rights reserved.
Deformation in locally convex topological linear spaces
Institute of Scientific and Technical Information of China (English)
DING; Yanheng
2004-01-01
We are concerned with a deformation theory in locally convex topological linear spaces. A special "nice" partition of unity is given. This enables us to construct certain vector fields which are locally Lipschitz continuous with respect to the locally convex topology. The existence, uniqueness and continuous dependence of flows associated to the vector fields are established. Deformations related to strongly indefinite functionals are then obtained. Finally, as applications, we prove some abstract critical point theorems.
The convexity radius of a Riemannian manifold
Dibble, James
2014-01-01
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.
Convexity conditions and normal structure of Banach spaces
Saejung, Satit
2008-08-01
We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure.
Entropy Coherent and Entropy Convex Measures of Risk
Laeven, R.J.A.; Stadje, M.A.
2011-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences, respe
A further characteristic of abstract convexity structures on topological spaces
Xiang, Shu-Wen; Xia, Shunyou
2007-11-01
In this paper, we give a characteristic of abstract convexity structures on topological spaces with selection property. We show that if a convexity structure defined on a topological space has the weak selection property then satisfies H0-condition. Moreover, in a compact convex subset of a topological space with convexity structure, the weak selection property implies the fixed point property.
Supply chain optimization: a practitioner's perspective on the next logistics breakthrough.
Schlegel, G L
2000-08-01
The objective of this paper is to profile a practitioner's perspective on supply chain optimization and highlight the critical elements of this potential new logistics breakthrough idea. The introduction will briefly describe the existing distribution network, and business environment. This will include operational statistics, manufacturing software, and hardware configurations. The first segment will cover the critical success factors or foundations elements that are prerequisites for success. The second segment will give you a glimpse of a "working game plan" for successful migration to supply chain optimization. The final segment will briefly profile "bottom-line" benefits to be derived from the use of supply chain optimization as a strategy, tactical tool, and competitive advantage.
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.
Fluctuations of collective coordinates and convexity theorems for energy surfaces
Giraud, B G; Sami, T
2016-01-01
Constrained energy minimizations of a many-body Hamiltonian return energy landscapes e(b) where b= representes the average value(s) of one (or several) collective operator(s), B, in an "optimized" trial state Phi_b, and e = is the average value of the Hamiltonian in this state Phi_b. It is natural to consider the uncertainty, Delta e, given that Phi_b usually belongs to a restricted set of trial states. However, we demonstrate that the uncertainty, Delta b, must also be considered, acknowledging corrections to theoretical models. We also find a link between fluctuations of collective coordinates and convexity properties of energy surfaces.
Sparse Signal Recovery from Quadratic Measurements via Convex Programming
Li, Xiaodong; Voroninski, Vladislav
2012-01-01
In this paper we consider a system of quadratic equations ||^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be underdetermined, i.e., m < n. We prove that if there exists a sparse solution x, i.e., at most k components of x are non-zero, then by solving a convex optimization program, we can solve for x up to a multiplicative constant with high probability, provided that k
Sidky, Emil Y; Pan, Xiaochuan
2012-01-01
Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this article, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for efficient algorithms for their solution -- thereby facilitating the IIR algorithm design process. An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex fea...
First-order convex feasibility algorithms for x-ray CT
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2013-01-01
Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times......, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems....... In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution—thereby facilitating...
Spectral calibration for convex grating imaging spectrometer
Zhou, Jiankang; Chen, Xinhua; Ji, Yiqun; Chen, Yuheng; Shen, Weimin
2013-12-01
Spectral calibration of imaging spectrometer plays an important role for acquiring target accurate spectrum. There are two spectral calibration types in essence, the wavelength scanning and characteristic line sampling. Only the calibrated pixel is used for the wavelength scanning methods and he spectral response function (SRF) is constructed by the calibrated pixel itself. The different wavelength can be generated by the monochromator. The SRF is constructed by adjacent pixels of the calibrated one for the characteristic line sampling methods. And the pixels are illuminated by the narrow spectrum line and the center wavelength of the spectral line is exactly known. The calibration result comes from scanning method is precise, but it takes much time and data to deal with. The wavelength scanning method cannot be used in field or space environment. The characteristic line sampling method is simple, but the calibration precision is not easy to confirm. The standard spectroscopic lamp is used to calibrate our manufactured convex grating imaging spectrometer which has Offner concentric structure and can supply high resolution and uniform spectral signal. Gaussian fitting algorithm is used to determine the center position and the Full-Width-Half-Maximum（FWHM）of the characteristic spectrum line. The central wavelengths and FWHMs of spectral pixels are calibrated by cubic polynomial fitting. By setting a fitting error thresh hold and abandoning the maximum deviation point, an optimization calculation is achieved. The integrated calibration experiment equipment for spectral calibration is developed to enhance calibration efficiency. The spectral calibration result comes from spectral lamp method are verified by monochromator wavelength scanning calibration technique. The result shows that spectral calibration uncertainty of FWHM and center wavelength are both less than 0.08nm, or 5.2% of spectral FWHM.
Stochastic convex sparse principal component analysis.
Baytas, Inci M; Lin, Kaixiang; Wang, Fei; Jain, Anil K; Zhou, Jiayu
2016-12-01
Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ℓ1 regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.
Empirical study on optimal reinsurance for crop insurance in China from an insurer’s perspective
Institute of Scientific and Technical Information of China (English)
ZHOU Xian-hua; WANG Yun-bo; ZHANG Hua-dong; WANG Ke
2015-01-01
This study investigates the optimal reinsurance for crop insurance in China in an insurer’s perspective using the data from Inner Mongolia, Jilin, and Liaoning, China. On the basis of the loss ratio distributions modeled by AnHua Crop Risk Evalu-ation System, we use the empirical model developed by Tan and Weng (2014) to study the optimal reinsurance design for crop insurance in China. We ifnd that, when the primary insurer’s loss function, the principle of the reinsurance premium calculation, and the risk measure are given, the level of risk tolerance of the primary insurer, the safety loading coefifcient of the reinsurer, and the constraint on reinsurance premium budget affect the optimal reinsurance design. When a strict constraint on reinsurance premium budget is implemented, which often occurs in reality, the limited stop loss reinsurance is optimal, consistent with the common practice in reality. This study provides suggestions for decision making regarding the crop reinsurance in China. It also provides empirical evidence for the literature on optimal reinsurance from the insurance market of China. This evidence undoubtedly has an important practical signiifcance for the development of China’s crop insurance.
The Duality on Vector Optimization Problems
Institute of Scientific and Technical Information of China (English)
HUANG Long-guang
2012-01-01
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
Cost Allocation and Convex Data Envelopment
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Tind, Jørgen
This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann-Shapley and the Friedman-Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming...... such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...... problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models...
Non-convex onion peeling using a shape hull algorithm
Fadili, Jalal M.; Melkemi, Mahmoud; Elmoataz, Abderrahim
2004-01-01
International audience; The convex onion-peeling of a set of points is the organization of these points into a sequence of interpolating convex polygons. This method is adequate to detect the shape of the “center” of a set of points when this shape is convex. However it reveals inadequate to detect non-convex shapes. Alternatively, we propose an extension of the convex onion-peeling method. It consists in representing a set of points with a sequence of non-convex polylines which are computed ...
Uniform convexity and the splitting problem for selections
Balashov, Maxim V; 10.1016/j.jmaa.2009.06.045
2009-01-01
We continue to investigate cases when the Repov\\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Cost Allocation and Convex Data Envelopment
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Tind, Jørgen
problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models...... such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output...
Convex functions and the rolling circle criterion
1995-01-01
Given 0≤R1≤R2≤∞, CVG(R1,R2) denotes the class of normalized convex functions f in the unit disc U, for which ∂f(U) satisfies a Blaschke Rolling Circles Criterion with radii R1 and R2. Necessary and sufficient conditions for R1=R2, growth and distortion theorems for CVG(R1,R2) and rotation theorem for the class of convex functions of bounded type, are found.
A Complete Characterization of the Gap between Convexity and SOS-Convexity
Ahmadi, Amir Ali
2011-01-01
Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials via the definition of convexity, its first order characterization, and its second order characterization are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\\tilde{C}_{n,d}$ and $\\tilde{\\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\\tilde{C}_{n,d}=\\tilde{\\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\\Sigma C_{...
Left ventricle segmentation in MRI via convex relaxed distribution matching.
Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben
2013-12-01
A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm
Bayoumi, A
2003-01-01
All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and
Chance-Constrained Guidance With Non-Convex Constraints
Ono, Masahiro
2011-01-01
Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of
Design of a flight control architecture using a non-convex bundle method
Gabarrou, Marion; Alazard, Daniel; Noll, Dominikus
2013-01-01
We design a feedback control architecture for longitudinal flight of an aircraft. The multi-level architecture includes the flight control loop to govern the short term dynamics of the aircraft, and the autopilot to control the long term modes. Using H1 performance and robustness criteria, the problem is cast as a non-convex and non-smooth optimization program. We present a non-convex bundle method, prove its convergence, and show that it is apt to solve the longitudinal flight control pro...
Sharp recovery bounds for convex deconvolution, with applications
McCoy, Michael B
2012-01-01
Deconvolution refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. A standard example is the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis. Another familiar case is the problem of decomposing an observed matrix into a low-rank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these deconvolution problems and many others. This work introduces a randomized signal model which ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, the calculus of spherical integral geometry provides an exact formula that describes when the optimization problem will succeed (or fail) to deconvolve the two constituent signals with high probability. This approach identifies a summary statistic that reflects the complexity of a particu...
Tropicalized Lambda Lengths, Measured Laminations and Convexity
DEFF Research Database (Denmark)
C. Penner, R.
cell decomposition of a surface is discovered in the limit. Finally, the tropical analogue of the convex hull construction in Minkowski space is formulated as an explicit algorithm that serially simplifies a triangulation with respect to a fixed lamination and has its own independent applications....
Some Characterizations of Convex Interval Games
Brânzei, R.; Tijs, S.H.; Alparslan-Gok, S.Z.
2008-01-01
This paper focuses on new characterizations of convex interval games using the notions of exactness and superadditivity. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of exactness and subadditivity.
Tropicalized Lambda Lengths, Measured Laminations and Convexity
DEFF Research Database (Denmark)
C. Penner, R.
This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension...
On fixed points and uniformly convex spaces
Gelander, Tsachik
2008-01-01
The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first $L_p$-cohomology of higher rank simple Lie groups, proved in [BFGM].
Dynamic Matchings in Convex Bipartite Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt
2007-01-01
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...
Minimizing convex functions by continuous descent methods
Directory of Open Access Journals (Sweden)
Sergiu Aizicovici
2010-01-01
Full Text Available We study continuous descent methods for minimizing convex functions, defined on general Banach spaces, which are associated with an appropriate complete metric space of vector fields. We show that there exists an everywhere dense open set in this space of vector fields such that each of its elements generates strongly convergent trajectories.
Differential analysis of matrix convex functions
DEFF Research Database (Denmark)
Hansen, Frank; Tomiyama, Jun
2007-01-01
We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for ma...
Estimates for oscillatory integrals with convex phase
Energy Technology Data Exchange (ETDEWEB)
Chakhkiev, M A [Moscow State Social University, Moscow (Russian Federation)
2006-02-28
We consider methods for estimating one-dimensional oscillatory integrals with convex phase and amplitudes of bounded variation or Lipschitz class amplitudes. In particular, we improve the estimate for the Piercey integral with near-caustic parameter values, and also consider estimation methods for n-dimensional oscillatory integrals.
Some Characterizations of Convex Interval Games
Brânzei, R.; Tijs, S.H.; Alparslan-Gok, S.Z.
2008-01-01
This paper focuses on new characterizations of convex interval games using the notions of exactness and superadditivity. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of exactness and subadditivity.
Convex bodies of states and maps
Grabowski, Janusz; Ibort, Alberto; Kuś, Marek; Marmo, Giuseppe
2013-10-01
We give a general solution to the question of when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density operators. The same approach can be applied to study convex combinations of quantum channels. The importance of both problems stems from the fact that, usually, only sets with non-vanishing volumes in the embedding spaces of all states or channels are of practical importance. For the group of local transformations on a bipartite system we characterize maximally entangled states by the properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of the largest balls and maximum volume ellipsoids contained in them and show that, in general, they do not coincide. Separable states, mixed-unitary channels and k-entangled states are also considered as examples of our techniques.
Convexity properties of Hamiltonian group actions
Guillemin, Victor
2005-01-01
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic&rdquo case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel sub...
A New Hybrid Shuffled Frog Leaping Algorithm to Solve Non-convex Economic Load Dispatch Problem
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Ehsan Bijami
2011-11-01
Full Text Available This paper presents a New Hybrid Shuffled Frog Leaping (NHSFL algorithm applied to solve Economic Load Dispatch (ELD problem. Practical ELD has non-convex cost function and various equality and inequality constraints that convert the ELD problem as a nonlinear, non-convex and non-smooth optimization problem. In this paper, a new frog leaping rule is proposed to improve the local exploration and the performance of the conventional SFL algorithm. Also a genetic mutation operator is used for the creation of new frogs instead of random frog creation that improves the convergence. To show the efficiency of the proposed approach, the non-convex ELD problem is solved using conventional SFL and an improved SFL method proposed by other researchers. Then the results of SFL methods are compared to the results obtained by the proposed NHSFL algorithm. Simulation studies show that the results obtained by NHSFL are more effective and better compared with these algorithms.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Inverse Optimization: A New Perspective on the Black-Litterman Model.
Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch
2012-12-11
The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct "BL"-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new "BL"-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views.
On the convexity of N-Chebyshev sets
Borodin, Petr A.
2011-10-01
We define N-Chebyshev sets in a Banach space X for every positive integer N (when N=1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N\\ge 3 is odd and X is smooth uniformly convex.
The Identification of Convex Function on Riemannian Manifold
Directory of Open Access Journals (Sweden)
Li Zou
2014-01-01
Full Text Available The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.
ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
Shen Xisheng; Cheng Lixin
2005-01-01
A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.
Xu, Lei
2007-02-01
According to the proof by Liu, Chiu, and Xu (2004) on the so-called one-bit-matching conjecture (Xu, Cheung, and Amari, 1998a), all the sources can be separated as long as there is an one-to-one same-sign correspondence between the kurtosis signs of all source probability density functions (pdf's) and the kurtosis signs of all model pdf's, which is widely believed and implicitly supported by many empirical studies. However, this proof is made only in a weak sense that the conjecture is true when the global optimal solution of an independent component analysis criterion is reached. Thus, it cannot support the successes of many existing iterative algorithms that usually converge at one of the local optimal solutions. This article presents a new mathematical proof that is obtained in a strong sense that the conjecture is also true when any one of local optimal solutions is reached in helping to investigating convex-concave programming on a polyhedral set. Theorems are also provided not only on partial separation of sources when there is a partial matching between the kurtosis signs, but also on an interesting duality of maximization and minimization on source separation. Moreover, corollaries are obtained on an interesting duality, with supergaussian sources separated by maximization and subgaussian sources separated by minimization. Also, a corollary is obtained to confirm the symmetric orthogonalization implementation of the kurtosis extreme approach for separating multiple sources in parallel, which works empirically but lacks mathematical proof. Furthermore, a linkage has been set up to combinatorial optimization from a distribution approximation perspective and a Stiefel manifold perspective, with algorithms that guarantee convergence as well as satisfaction of constraints.
Geometry intuitive, discrete, and convex : a tribute to László Fejes Tóth
Böröczky, Károly; Tóth, Gábor; Pach, János
2013-01-01
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.
Allometric relationships between traveltime channel networks, convex hulls, and convexity measures
Tay, Lea Tien; Sagar, B. S. Daya; Chuah, Hean Teik
2006-06-01
The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and areas of corresponding convex hulls C(Sn), the ratios of which provide convexity measures CM(Sn) of traveltime networks. A statistically significant scaling relationship is found for a model network in the form L(Sn) ˜ A[C(Sn)]0.57. From the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures, new power law relations are derived. Such relations for a model network are CM(Sn) ˜ ? and CM(Sn) ˜ ?. In addition to the model study, these relations for networks derived from seven subbasins of Cameron Highlands region of Peninsular Malaysia are provided. Further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks.
Institute of Scientific and Technical Information of China (English)
刘雄厚; 孙超; 卓颉; 邵炫; 谢磊
2013-01-01
A receiver design method based on the “mismatched” filtering processing is proposed for the multiple -in-put multiple-output (MIMO) sonar imaging application.To calculate the coefficients of the “mismatched” filter, the convex optimization method is adopted .Via numerical simulations, we show that the “mismatched” filter can suppress the sidelobes of outputs at the cost of sacrificing some white Gaussian noise gain , which is tolerable for the sonar imaging application.And thus, compared to a matched filter, better sidelobe suppression effect in the ima -ging result is obtained by using the “mismatched” filter.% 提出了利用失配滤波处理来设计多输入多输出（Multiple-Input Multiple-Output：MIMO）成像声纳的接收滤波器，并采用 cvx 工具箱来求解滤波器的系数。与匹配滤波处理相比，在牺牲一定高斯白噪声增益的前提下，失配滤波处理成功抑制了相关输出的旁瓣级。仿真结果表明，所提出的失配滤波处理方法可以有效抑制 MIMO 声纳成像结果中的距离旁瓣干扰。
A Generalization of Uniformly Extremely Convex Banach Spaces
Suyalatu Wulede; Wurichaihu Bai; Wurina Bao
2016-01-01
We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes of k-uniformly rotund spaces and k-strongly convex spaces or classes of fully k-convex spaces and k-strongly convex spaces and has no inclusive relation with the class of locally k-uniformly convex spaces. We obtain in addition some characterizations and properties of this ne...
Input Design for System Identification via Convex Relaxation
Manchester, Ian R
2010-01-01
This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal senses. In contrast to the majority of published work on this topic, we consider the problem in the time domain and subject to constraints on the amplitude of the input signal. This optimization problem is nonconvex. The main result of the paper is a convex relaxation that gives an upper bound accurate to within $2/\\pi$ of the true maximum. A randomized algorithm is presented for finding a feasible solution which, in a certain sense is expected to be at least $2/\\pi$ as informative as the globally optimal input signal. In the case of a single constraint on input power, the proposed approach recovers the true global optimum exactly. Extensions to situations with both power and amplitude constraints on both inputs and outputs are given. A simple simulation example illustrates th...
A note of well-posedness and convexity on vector optimization%关于向量优化的适定性和凸性的一个注记
Institute of Scientific and Technical Information of China (English)
韩瑜; 邬建军; 龚循华
2014-01-01
举出一个反例说明在论文（Math Meth Oper Res，2003，58：375－385）中，关于向量优化问题的适定性的一个主要结果是错的。%In this notepaper,we gave gave a counterexample to illustrate that a main result for well-posedn-ess on vector optimization problems presented in (Math Meth Oper Res,2003,58:375-385)was not cor-rect.
Brasco, Lorenzo
2012-01-01
We investigate some basic properties of the {\\it heart} $\\heartsuit(\\mathcal{K})$ of a convex set $\\mathcal{K}.$ It is a subset of $\\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\\heartsuit(\\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\\heartsuit(\\mathcal{K})$ and the mirror symmetries of $\\mathcal{K};$ we show that $\\heartsuit(\\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\\heartsuit(\\mathcal{K});$ we also prove an upper estimate for the area of $\\heartsuit(\\mathcal{K}),$ when $\\mathcal{K}$ is a triangle.
Coalescence between two convex liquid surfaces
Yang, Fan; Jian, Zhen; Li, Erqiang; Thoroddsen, S. T.
2015-11-01
We study the coalescence of two convex surfaces of the same liquid. One of the convex free surfaces is formed at a circular opening of a closed tank by imposing a negative pressure difference. The other surface is a droplet of larger curvature, which is pendant from a concentric nozzle. The coalescence starts from near-zero velocity, so the configuration can be characterized by two dimensionless numbers: the Ohnesorge number Oh = μ /√{ ργL } and the radius ratio between the two surfaces α =rd /rs . We use high-speed video, PIV and numerical simulations, using the Gerris program, to study the dynamics of the coalescence. Our focus is on the interface shapes, the growth-rate of the neck connecting the two surfaces and the formation of a vortex ring. The growth-rate is compared to earlier models for the coalescence of drops or bubbles.
Convex Arrhenius plots and their interpretation
Truhlar, Donald G.; Kohen, Amnon
2001-01-01
This paper draws attention to selected experiments on enzyme-catalyzed reactions that show convex Arrhenius plots, which are very rare, and points out that Tolman's interpretation of the activation energy places a fundamental model-independent constraint on any detailed explanation of these reactions. The analysis presented here shows that in such systems, the rate coefficient as a function of energy is not just increasing more slowly than expected, it is actually decreasing. This interpretation of the data provides a constraint on proposed microscopic models, i.e., it requires that any successful model of a reaction with a convex Arrhenius plot should be consistent with the microcanonical rate coefficient being a decreasing function of energy. The implications and limitations of this analysis to interpreting enzyme mechanisms are discussed. This model-independent conclusion has broad applicability to all fields of kinetics, and we also draw attention to an analogy with diffusion in metastable fluids and glasses. PMID:11158559
On the convexity of Relativistic Hydrodynamics
Ibáñez, José María; Martí, José María; Miralles, Juan Antonio; 10.1088/0264-9381/30/5/057002
2013-01-01
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\\it Rev. Mod. Phys.} {\\bf 61} 75). The classical limit is recovered.
Coefficient inequalities for starlikeness and convexity
Directory of Open Access Journals (Sweden)
Ali Rosihan M.
2013-06-01
Full Text Available For an analytic function $f(z=z+\\sum_{n=2}^\\infty a_n z^n$ satisfying the inequality $\\sum_{n=2}^\\infty n(n-1|a_n|\\leq \\beta$, sharp bound on $\\beta$ is determined so that $f$ is either starlike or convex of order $\\alpha$. Several other coefficient inequalities related to certain subclasses are also investigated.
When is multidimensional screening a convex program?
Figalli, Alessio; McCann, Robert J
2009-01-01
A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose only pure strategies, we identify a structural condition on the preference b(x,y) of agent type x for product type y -- and on the principal's costs c(y) -- which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal's problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal's optimum strategy -- and similarly of the strategy maximizing the expected welfare of the agents when the principal's profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under r...
Hyperspectral image superresolution: An edge-preserving convex formulation
Simões, Miguel; Almeida, Luis B; Chanussot, Jocelyn
2014-01-01
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of images with high spatial and spectral resolutions from HSI-MSI pairs. In this paper, we formulate this data fusion problem as the minimization of a convex objective function containing two data-fitting terms and an edge-preserving regularizer. The data-fitting terms are quadratic and account for blur, different spatial resolutions, and additive noise; the regularizer, a form of vector Total Variation, promotes aligned discontinuities across the reconstructed hyperspectral bands. The optimization described above is rather hard, owing to its non-diagonalizable linear operators, to the non-quadratic and non-smooth nature of the regularizer, and to the very large size of the image to be inferred. We tac...
Extreme properties of quermassintegrals of convex bodies
Institute of Scientific and Technical Information of China (English)
LENG; Gangsong
2001-01-01
［1］Ball,K.,Shadows of convex bodies,Trans.Amer.Math.Soc.,1991,327:891-901.［2］Lutwak,E.,Mixed projection inequalities,Trans.Amer.Math.Soc.,1985,287:92-106.［3］Bourgain,J.,Lindenstrauss,J.,Projection bodies,Israel Seminar (G.A.F.A) 1986-1987,Lecture Notes in Math.Vol.1317,Berlin-New York:Springer-Verlag,1988,250-269.［4］Chakerian,G.D.,Lutwak,E.,Bodies with similar projections,Trans.Amer.Math.Soc.,1997,349:1811-1820.［5］Schneider,R.,Weil,W.,Zonoids and related topics,Convexity and its Applications (eds.Gruber,P.M.,Wills,J.M.),Basel:Birkhuser,1983,296-316.［6］Schneider,R.,Convex Bodies:the Brunn-Minkowski Theory,Cambridge:Cambridge University Press,1993.［7］Schneider,R.,On the determination of convex bodies by projection and girth functions,Result Math.,1998,33:155-160.［8］Thompson,A.C.,Minkowski Geometry,Cambridge:Cambridge University Press,1996.［9］Petty,C.M.,Projection bodies,in Proceedings,Coll Convexity,Copenhagen,1965,Kbenhavns Univ.Mat.Inst.,1967,234-241.［10］Schneider,R.,Zu einem problem von Shephard über die projectionen konvexer kirper,Math.Z.,1967,101:71-81.［11］Ball,K.,Volume ratios and a reverse isoprimetric inequalitity,J.London Math.Soc.,1991,44(2):351-359.［12］Gardner,R.J.,Intersection bodies and the Busemann-Petty problem,Trans.Amer.Math.Soc.,1994,342:435-445.［13］Gardner,R.J.,A positive answer to the Busemann-petty problem in three dimensions,Annals of Math.,1994,140:435-447.［14］Grinberg,E.L.,Isoperimetric inequalities and identities fork-dimensional cross-sections of convex bodies,Math.Ann.,1991,291:75-86.［15］Goodey,P.,Schneider,R.,Weil,W.,On the determination of convex bodies by projection functions,Bull.London Math.Soc.,1997,29:82-88.［16］Lutwak,E.,Intersection bodies and dual mixed volumes,Adv.Math.,1988,71:232-261.［17］Zhang,G.,Centered bodies and dual mixed volumes,Trans.Amer.Soc.,1994,345:777-801.［18］Zhang,G.,Dual Kinematic formulas,Trans.Amer.Soc.,1999,351:985-995.［19
Optimization of formulation and process variable of nanosuspension: An industrial perspective.
Singare, Dhananjay S; Marella, Seshasai; Gowthamrajan, K; Kulkarni, Giriraj T; Vooturi, Rajesh; Rao, Parchuri Srinivasa
2010-12-15
The objective of this study was to identify and optimize formulation and process variables affecting characteristic and scale up of nanosuspension manufacturing process on bead mill considering industrial perspective. Box-Behnken design was used for this study. Formulation factors evaluated were ratio of polymer to drug and ratio of surfactant to drug, whereas process parameters were milling time and milling speed. Responses measured in this study include zeta potential and, particle size distribution d(90). The ANOVA test reveals that ratio of polymer to drug and milling speed has significant effect on zeta potential whereas milling time and milling speed has significant effect on the particle size distribution of nanosuspension. The X-RD pattern of drug milled at high and low speed reveals no form conversion when compared to unmilled drug. The Box-Behnken design used in this study helped in identifying the factors affecting the particle size distribution d(90), zeta potential and, scalability of nanosuspension. The derived polynomial equation and contour graph aid in predicting the values of selected independent variables for preparation of optimum nanosuspension formulations with desired properties.
Optimal management of breast cancer in the elderly patient: current perspectives
Directory of Open Access Journals (Sweden)
Le Saux O
2015-01-01
Full Text Available Olivia Le Saux,1 Bertrand Ripamonti,2 Amandine Bruyas,3,4 Olivier Bonin,4 Gilles Freyer,1,4 Marc Bonnefoy,4,5 Claire Falandry4,51Medical Oncology Unit, Lyon Sud University Hospital, Hospices Civils de Lyon, Pierre-Bénite, 2Gynaecology-Obstetrics Department, University Hospital, Saint-Etienne, 3Croix Rousse University Hospital, Hospices Civils de Lyon, Pierre-Bénite, 4Lyon University, Lyon, 5Geriatric Unit, Lyon Sud University Hospital, Hospices Civils de Lyon, Pierre-Bénite, FranceAbstract: Breast cancer (BC is the most common female malignancy in the world and almost one third of cases occur after 70 years of age. Optimal management of BC in the elderly is a real challenge and requires a multidisciplinary approach, mainly because the elderly population is heterogeneous. In this review, we describe the various possibilities of treatment for localized or metastatic BC in an aging population. We provide an overview of the comprehensive geriatric assessment, surgery, radiotherapy, and adjuvant therapy for early localized BC and of chemotherapy and targeted therapies for metastatic BC. Finally, we attempt to put into perspective the necessary balance between the expected benefits and risks, especially in the adjuvant setting.Keywords: elderly, breast cancer, geriatric assessment, surgery, chemotherapy, radiotherapy
Directory of Open Access Journals (Sweden)
Satit Saejung
2005-01-01
Full Text Available We prove that the moduli of U-convexity, introduced by Gao (1995, of the ultrapower X˜ of a Banach space X and of X itself coincide whenever X is super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1>0 implies that both X and the dual space X∗ of X have uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán-Navarro (2003 can be discarded.
Convex and Radially Concave Contoured Distributions
Directory of Open Access Journals (Sweden)
Wolf-Dieter Richter
2015-01-01
Full Text Available Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in Rn. As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.
Width Distributions for Convex Regular Polyhedra
Finch, Steven R
2011-01-01
The mean width is a measure on three-dimensional convex bodies that enjoys equal status with volume and surface area [Rota]. As the phrase suggests, it is the mean of a probability density f. We verify formulas for mean widths of the regular tetrahedron and the cube. Higher-order moments of f_tetra and f_cube have not been examined until now. Assume that each polyhedron has edges of unit length. We deduce that the mean square width of the regular tetrahedron is 1/3+(3+sqrt(3))/(3*pi) and the mean square width of the cube is 1+4/pi.
Measuring Voting Power in Convex Policy Spaces
Directory of Open Access Journals (Sweden)
Sascha Kurz
2014-03-01
Full Text Available Classical power index analysis considers the individual’s ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either “yes” or “no”. Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like, e.g., tax rates or spending that otherwise would not be covered in binary models.
Trace-Inequalities and Matrix-Convex Functions
Directory of Open Access Journals (Sweden)
Ando Tsuyoshi
2010-01-01
Full Text Available Abstract A real-valued continuous function on an interval gives rise to a map via functional calculus from the convex set of Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: for . A related topic will be also discussed.
Lower Bound for Convex Hull Area and Universal Cover Problems
Khandhawit, Tirasan; Sriswasdi, Sira
2011-01-01
In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.
Approximation of Convex Bodies by Convex Bodies%凸体间的逼近
Institute of Scientific and Technical Information of China (English)
国起; Sten Kaijser
2003-01-01
For the affine distance d(C,D)between two convex bodies C,D(∈)Rn,which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C,D)have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C,D)≤n1/2 if one is an ellipsoid and another is symmetric,d(C,D)≤n if both are symmetric, and fromF. John's result and d(C1,C2)≤d(C1,C3)d(C2,C3) one has d(C,D)≤n2 for general convex bodies;M.Lassak proved d(C,D)≤(2n-1) if one of them is symmetric.In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies.
Directory of Open Access Journals (Sweden)
Ryan Wen Liu
2017-03-01
Full Text Available Dynamic magnetic resonance imaging (MRI has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.
Liu, Ryan Wen; Shi, Lin; Yu, Simon Chun Ho; Xiong, Naixue; Wang, Defeng
2017-01-01
Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments. PMID:28273827
Path Following in the Exact Penalty Method of Convex Programming.
Zhou, Hua; Lange, Kenneth
2015-07-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.
Fu, Chun; Shuai, Zhenzhen
2015-01-01
Purpose: By studying the case of a Changsha engineering machinery manufacturing firm, this paper aims to find out the optimization tactics to reduce enterprise’s logistics operational cost. Design/methodology/approach: This paper builds the structure model of manufacturing enterprise’s logistics operational costs from the perspective of social firm network and simulates the model based on system dynamics. Findings: It concludes that applying system dynamics in the research o...
Long Wave Dynamics along a Convex Bottom
Didenkulova, Ira; Soomere, Tarmo
2008-01-01
Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the uniqueness of this wave class is established through construction of a 1:1 transformation of the general 1D wave equation to the analogous wave equation with constant coefficients. The general solution of the Cauchy problem consists of two travelling waves propagating in opposite directions. It is found that generally a zone of a weak current is formed between these two waves. Waves are reflected from the coastline so that their profile is inverted with respect to the calm water surface. Long wave runup on a beach with this profile is studied for sine pulse, KdV soliton and N-wave. Shown is that in certain cases the runup height along the convex profile is considerably larger than for beaches with a linear slope. The analysis of wave reflection from the bottom containing a s...
Molecular Graphics of Convex Body Fluids.
Gabriel, Adrian T; Meyer, Timm; Germano, Guido
2008-03-01
Coarse-grained modeling of molecular fluids is often based on nonspherical convex rigid bodies like ellipsoids or spherocylinders representing rodlike or platelike molecules or groups of atoms, with site-site interaction potentials depending both on the distance among the particles and the relative orientation. In this category of potentials, the Gay-Berne family has been studied most extensively. However, conventional molecular graphics programs are not designed to visualize such objects. Usually the basic units are atoms displayed as spheres or as vertices in a graph. Atomic aggregates can be highlighted through an increasing amount of stylized representations, e.g., Richardson ribbon diagrams for the secondary structure of proteins, Connolly molecular surfaces, density maps, etc., but ellipsoids and spherocylinders are generally missing, especially as elementary simulation units. We fill this gap providing and discussing a customized OpenGL-based program for the interactive, rendered representation of large ensembles of convex bodies, useful especially in liquid crystal research. We pay particular attention to the performance issues for typical system sizes in this field. The code is distributed as open source.
A new corrective technique for adolescent idiopathic scoliosis (Ucar′s convex rod rotation
Directory of Open Access Journals (Sweden)
Bekir Yavuz Ucar
2014-01-01
Full Text Available Study Design: Prospective single-center study. Objective: To analyze the efficacy and safety of a new technique of global vertebral correction with convex rod rotation performed on the patients with adolescent idiopathic scoliosis. Summary of Background Data: Surgical goal is to obtain an optimal curve correction in scoliosis surgery. There are various correction techniques. This report describes a new technique of global vertebral correction with convex rod rotation. Materials and Methods: A total of 12 consecutive patients with Lenke type I adolescent idiopathic scoliosis and managed by convex rod rotation technique between years 2012 and 2013 having more than 1 year follow-up were included. Mean age was 14.5 (range = 13-17 years years at the time of operation. The hospital charts were reviewed for demographic data. Measurements of curve magnitude and balance were made on 36-inch standing anteroposterior and lateral radiographs taken before surgery and at most recent follow up to assess deformity correction, spinal balance, and complications related to the instrumentation. Results: Preoperative coronal plane major curve of 62° (range = 50°-72° with flexibility of less than 30% was corrected to 11.5°(range = 10°-14° showing a 81% scoliosis correction at the final follow-up. Coronal imbalance was improved 72% at the most recent follow-up assessment. No complications were found. Conclusion: The new technique of global vertebral correction with Ucar′s convex rod rotation is an effective technique. This method is a vertebral rotation procedure from convex side and it allows to put screws easily to the concave side.
Convex Optimization methods for computing the Lyapunov Exponent of matrices
Protasov, Vladimir Yu
2012-01-01
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for the Lyapunov exponent. They improve previously known bounds and converge to the real value. The rate of convergence is estimated and the efficiency of the algorithm is demonstrated on several problems from applications (in functional analysis, combinatorics, and lan- guage theory) and on numerical examples with randomly generated matrices. The method computes the Lyapunov exponent with a prescribed accuracy in relatively high dimensions (up to 60). We generalize this approach to all matrices, not necessar- ily nonnegative, derive a new universal upper bound for the Lyapunov exponent, and show that such a lower bound, in general, does not exist.
Convex Optimization Methods for Graphs and Statistical Modeling
2011-06-01
requirements that the graph be triangle-free and square-free. Of course such graph reconstruction problems may be infeasible in general, as there may be...over C1, C2 is motivated by a similar procedure in statistics and signal processing, which goes by the name of “matched filtering.” Of course other...h is the height of the cap over the equator. Via elementary trigonometry , the solid angle that K subtends is given by π/2 − sin−1(h). Hence, if h(β
Multivariable robust digital controller design by convex optimization
2004-01-01
The dissertation is essentially concerned with methods of robust digital multivariable and monovariable controller design. For controller desing, a linear discrete-time model of plant to be controlled is used. The controller robustness is treated by sensitivity frequency analysis(sensitivity is transfer function/matrix of closed loop). Correspondingly to H∞ design, the singular values of frequency responses are used for the analysis.The work is divided into five parts. The first part concerns...
Greedy vs. L1 convex optimization in sparse coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor;
2015-01-01
through finding the L0-norm solution of the problem: min ||Y -D_{alpfa}||–2^2 +||alpha||_0, is crucial. Note that D refers to the dictionary and refers to the sparse codes. This L0-norm solution, however, is known as a NP-hard problem. Despite of the research achievements in some classification fields...
Directory of Open Access Journals (Sweden)
Chun Fu
2015-05-01
Full Text Available Purpose: By studying the case of a Changsha engineering machinery manufacturing firm, this paper aims to find out the optimization tactics to reduce enterprise’s logistics operational cost. Design/methodology/approach: This paper builds the structure model of manufacturing enterprise’s logistics operational costs from the perspective of inter-firm network and simulates the model based on system dynamics. Findings: It concludes that applying system dynamics in the research of manufacturing enterprise’s logistics cost control can better reflect the relationship of factors in the system. And the case firm can optimize the logistics costs by implement joint distribution. Research limitations/implications: This study still lacks comprehensive consideration about the variables quantities and quantitative of the control factors. In the future, we should strengthen the collection of data and information about the engineering manufacturing firms and improve the logistics operational cost model. Practical implications: This study puts forward some optimization tactics to reduce enterprise’s logistics operational cost. And it is of great significance for enterprise’s supply chain management optimization and logistics cost control. Originality/value: Differing from the existing literatures, this paper builds the structure model of manufacturing enterprise’s logistics operational costs from the perspective of inter-firm network and simulates the model based on system dynamics.
Convexity-preserving Bernstein–Bézier quartic scheme
Directory of Open Access Journals (Sweden)
Maria Hussain
2014-07-01
Full Text Available A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Bézier quartic function is used for interpolation. Lower bound of the boundary and inner Bézier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints.
Finding sets of points without empty convex 6-gons
Overmars, M.H.
2001-01-01
Erdös asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast
Convex bodies in Euclidean and Weil-Petersson geometries
Yamada, Sumio
2011-01-01
On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting metric structure shares with Thurston's asymmetric metric is noted.
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 ...
In-vivo Convex Array Vector Flow Imaging
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Brandt, Andreas Hjelm; Nielsen, Michael Bachmann
2014-01-01
In-vivo VFI scans obtained from the abdomen of a human volunteer using a convex array transducers and trans- verse oscillation vector flow imaging (VFI) are presented. A 3 MHz BK Medical 8820e (Herlev, Denmark) 192-element convex array probe is used with the SARUS experimental ultrasound scanner....
Locally uniformly convex norms in Banach spaces and their duals
Haydon, Richard
2006-01-01
It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions.
On a-order-convexity of Fuzzy Syntopogenous Spaces
Institute of Scientific and Technical Information of China (English)
WANG Hong
2007-01-01
In this paper,we combine L-fuzzy syntopogenous structure on X with algebraic structure on X.First,the *-increasing and *-decreasing spaces have been studied.Second,we define a-order-convexity on syntopogenous structures (X,S,≤).some important properties of a-order-convexity have been obtained.
Infinitesimal nonrigidity of convex surfaces with planar boundary
Institute of Scientific and Technical Information of China (English)
LI Chunhe; HONG Jiaxing
2005-01-01
In the present paper infinitesimal nonrigidity of a class of convex surfaces with planar boundary is given. This result shows that if the image of the Gauss map of an evolution convex surface with planar boundary covers some hemisphere, this surface may be of infinitesimal nonrigidity for the isometric deformation of planar boundary.
Homotopy Method for Non-convex Programming in Unbonded Set
Institute of Scientific and Technical Information of China (English)
徐庆; 于波
2005-01-01
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
(Average-) convexity of common pool and oligopoly TU-games
Driessen, T.S.H.; Meinhardt, H.
2000-01-01
The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the rele
Simple sufficient conditions for starlikeness and convexity for meromorphic functions
Directory of Open Access Journals (Sweden)
Goswami Pranay
2016-01-01
Full Text Available In this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.
Institute of Scientific and Technical Information of China (English)
Jinqian; DENG; Kangkang; SHAN; Yan; ZHANG
2014-01-01
The rural fundamental and productive fixed-asset investment not only makes active influence on the changes of farmers’ operational,wages and property income,but it also has an optimal scale range for farmers’ income increase. From the perspective of farmers’ income increase,this article evaluates the optimal scale of rural fixed-asset investment by setting up model with statistic data,and the results show that the optimal scale of per capita rural fixed-asset investment is 76. 35% of per capita net income of rural residents,which has been reached in China in 2009. Therefore,compared with the adding of rural fixed-asset investment,a better income increase effect can be achieved through the adjustment of rural fixed-asset investment structure.
The inverse moment problem for convex polytopes
Gravin, Nick; Pasechnik, Dmitrii; Robins, Sinai
2011-01-01
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.
non-Lipschitzian mappings without convexity
Directory of Open Access Journals (Sweden)
G. Li
1999-01-01
real Hilbert space H, and ℑ={Tt:t∈G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x={z∈H:infs∈Gsupt∈G‖Tts x−z‖=inft∈G‖Tt x−z‖} for each x∈C and L(ℑ=∩x∈C L(x. In this paper, we prove that ∩s∈Gconv¯{Tts x:t∈G}∩L(ℑ is nonempty for each x∈C if and only if there exists a unique nonexpansive retraction P of C into L(ℑ such that PTs=P for all s∈G and P(x∈conv¯{Ts x:s∈G} for every x∈C. Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.
DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Jacek DZIOK; Ravinder Krishna RAINA; Janusz SOK(O)L
2013-01-01
This article presents some new results on the class SLMα of functions that are analytic in the open unit discu ={z:[z[＜ 1} satisfying the conditions that f(0)=0,f'(0)=1,and α (1+ zf"(z)/f'(z)) + (1-α)zf'(z)/f(x) ∈(p)(u)for all z ∈ u,where α is a real number and (p)(z) =1 + τ2z2/ 1-τz-τ2z2 (z ∈ u).The number τ =(1-√5)/2 is such that τ2 =1 + T.The class SLMα introduced by J.Dziok,R.K.Raina,and J.Sokól [3,Appl.Math.Comput.218 (2011),996-1002] is closely related to the classes of starlike and convex functions.The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.
Quantification of small, convex particles by TEM
Energy Technology Data Exchange (ETDEWEB)
Andersen, Sigmund J. [SINTEF Materials and Chemistry, Department of Synthesis and Properties, Material Physics, NO-7465 Trondheim (Norway)], E-mail: sigmund.j.andersen@sintef.no; Holme, Borge [SINTEF Materials and Chemistry, P.O. Box 124, Blindern, NO-0314 Oslo (Norway); Marioara, Calin D. [SINTEF Materials and Chemistry, Department of Synthesis and Properties, Material Physics, NO-7465 Trondheim (Norway)
2008-07-15
It is shown how size distributions of arbitrarily oriented, convex, non-overlapping particles extracted from conventional transmission electron microscopy (TEM) images may be determined by a variation of the Schwartz-Saltykov method. In TEM, particles cut at the surfaces have diminished projections, which alter the observed size distribution. We represent this distribution as a vector and multiply it with the inverse of a matrix comprising thickness-dependent Scheil or Schwartz-Saltykov terms. The result is a corrected size distribution of the projections of uncut particles. It is shown how the real (3D) distribution may be estimated when particle shape is considered. Computer code to generate the matrix is given. A log-normal distribution of spheres and a real distribution of pill-box-shaped dispersoids in an Al-Mg-Si alloy are given as examples. The errors are discussed in detail.
Weighted composition operators and locally convex algebras
Institute of Scientific and Technical Information of China (English)
Edoardo Vesentini
2005-01-01
The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A: A → A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.
The problem of convexity of Chebyshev sets
Balaganskii, V. S.; Vlasov, L. P.
1996-12-01
Contents Introduction §1. Definitions and notation §2. Reference theorems §3. Some results Chapter I. Characterization of Banach spaces by means of the relations between approximation properties of sets §1. Existence, uniqueness §2. Prom approximate compactness to 'sun'-property §3. From 'sun'-property to approximate compactness §4. Differentiability in the direction of the gradient is sufficient for Fréchet and Gâteaux differentiability §5. Sets with convex complement Chapter II. The structure of Chebyshev and related sets §1. The isolated point method §2. Restrictions of the type \\vert\\overline{W}\\vert Klee (discrete Chebyshev set) §4. A survey of some other results Conclusion Bibliography
Convex Decomposition Based Cluster Labeling Method for Support Vector Clustering
Institute of Scientific and Technical Information of China (English)
Yuan Ping; Ying-Jie Tian; Ya-Jian Zhou; Yi-Xian Yang
2012-01-01
Support vector clustering (SVC) is an important boundary-based clustering algorithm in multiple applications for its capability of handling arbitrary cluster shapes. However,SVC's popularity is degraded by its highly intensive time complexity and poor label performance.To overcome such problems,we present a novel efficient and robust convex decomposition based cluster labeling (CDCL) method based on the topological property of dataset.The CDCL decomposes the implicit cluster into convex hulls and each one is comprised by a subset of support vectors (SVs).According to a robust algorithm applied in the nearest neighboring convex hulls,the adjacency matrix of convex hulls is built up for finding the connected components; and the remaining data points would be assigned the label of the nearest convex hull appropriately.The approach's validation is guaranteed by geometric proofs.Time complexity analysis and comparative experiments suggest that CDCL improves both the efficiency and clustering quality significantly.
ANALYSIS TO NEYMAN-PEARSON CLASSIFICATION WITH CONVEX LOSS FUNCTION
Institute of Scientific and Technical Information of China (English)
Min Han; Dirong Chen; Zhaoxu Sun
2008-01-01
Neyman-Pearson classification has been studied in several articles before.But they all proceeded in the classes of indicator functions with indicator function as the loss function,which make the calculation to be difficult.This paper investigates NeymanPearson classification with convex loss function in the arbitrary class of real measurable functions.A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function.We give analysis to NP-ERM with convex loss function and prove it's performance guarantees.An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied,which produces a tight PAC bound of the NP-ERM with convex loss function.
Efficient protocols for point-convex hull inclusion decision problems
Directory of Open Access Journals (Sweden)
Yun Ye
2010-05-01
Full Text Available Secure Multi-party Computation (SMC is dedicated to solve trust problems in cooperative computing with each participant’s private data. Privacy Preserving Computational Geometry (PPCG is a special area in SMC and being widely researched. In the real world, PPCG theories can be found being used in various occasions such as military cooperation, commercial competitions and so on. Point-convex hull inclusion problem is a practical case in PPCG and has its profound values. This paper firstly investigates the point inclusion problem with static convex hull, and then marches on to the cases of active convex hull, including the parallel moving and rotating ones. To solve the problems above, we propose a secure protocol to determine the relative position of a private point and a private convex hull in the first place. Compared with previous solutions, our protocols perform better in efficiency, especially when the number of the convex hull’s point is large.
Misunderstanding that the Effective Action is Convex under Broken Symmetry
Asanuma, Nobu-Hiko
2016-01-01
The widespread belief that the effective action is convex and has a flat bottom under broken global symmetry is shown to be wrong. We show spontaneous symmetry breaking necessarily accompanies non-convexity in the effective action for quantum field theory, or in the free energy for statistical mechanics, and clarify the magnitude of non-convexity. For quantum field theory, it is also explicitly proved that translational invariance breaks spontaneously when the system is in the non-convex region, and that different vacua of spontaneously broken symmetry cannot be superposed. As applications of non-convexity, we study the first-order phase transition which happens at the zero field limit of spontaneously broken symmetry, and we propose a simple model of phase coexistence which obeys the Born rule.
CPU timing routines for a CONVEX C220 computer system
Bynum, Mary Ann
1989-01-01
The timing routines available on the CONVEX C220 computer system in the Structural Mechanics Division (SMD) at NASA Langley Research Center are examined. The function of the timing routines, the use of the timing routines in sequential, parallel, and vector code, and the interpretation of the results from the timing routines with respect to the CONVEX model of computing are described. The timing routines available on the SMD CONVEX fall into two groups. The first group includes standard timing routines generally available with UNIX 4.3 BSD operating systems, while the second group includes routines unique to the SMD CONVEX. The standard timing routines described in this report are /bin/csh time,/bin/time, etime, and ctime. The routines unique to the SMD CONVEX are getinfo, second, cputime, toc, and a parallel profiling package made up of palprof, palinit, and palsum.
Usami, Yumi; Stork, David G.; Fujiki, Jun; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru
2011-03-01
We derive and demonstrate new methods for dewarping images depicted in convex mirrors in artwork and for estimating the three-dimensional shapes of the mirrors themselves. Previous methods were based on the assumption that mirrors were spherical or paraboloidal, an assumption unlikely to hold for hand-blown glass spheres used in early Renaissance art, such as Johannes van Eyck's Portrait of Giovanni (?) Arnolfini and his wife (1434) and Robert Campin's Portrait of St. John the Baptist and Heinrich von Werl (1438). Our methods are more general than such previous methods in that we assume merely that the mirror is radially symmetric and that there are straight lines (or colinear points) in the actual source scene. We express the mirror's shape as a mathematical series and pose the image dewarping task as that of estimating the coefficients in the series expansion. Central to our method is the plumbline principle: that the optimal coefficients are those that dewarp the mirror image so as to straighten lines that correspond to straight lines in the source scene. We solve for these coefficients algebraically through principal component analysis, PCA. Our method relies on a global figure of merit to balance warping errors throughout the image and it thereby reduces a reliance on the somewhat subjective criterion used in earlier methods. Our estimation can be applied to separate image annuli, which is appropriate if the mirror shape is irregular. Once we have found the optimal image dewarping, we compute the mirror shape by solving a differential equation based on the estimated dewarping function. We demonstrate our methods on the Arnolfini mirror and reveal a dewarped image superior to those found in prior work|an image noticeably more rectilinear throughout and having a more coherent geometrical perspective and vanishing points. Moreover, we find the mirror deviated from spherical and paraboloidal shape; this implies that it would have been useless as a concave
Loyka, Sergey; Gagnon, Francois
2009-01-01
Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fa...
Institute of Scientific and Technical Information of China (English)
Zhiping Qiu; Xiaojun Wang
2006-01-01
Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations.The results of this study indicate mat under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width Of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.
Convex objective function-based design method developed for minimizing side lobe.
Liu, Jian; Tan, Jiubin; Zhao, Chenguang
2008-08-01
The existence of multiple local solutions makes it very difficult to search for filter parameters to achieve a desired side lobe level during the design of superresolution pupil filters. To deal with the difficult issue of side lobe control in the designing process, a convex objective function-based design method is developed through phase rotation and variable replacement to transform the complicated solving process with multiextreme subintervals into a simple optimization process with a convex interval. A group of constant annular complex superresolving filters are designed using the developed method. The comparison of the superresolving filters designed in this way with the well-known continuous phase filter and 3-zone multiphase diffractive superresolution filters proves the validity of the developed method.
Goberna, Miguel A.; Jeyakumar, Vaithilingam; Li, Guoyin; Linh, Nguyen
2016-01-01
The radius of robust feasibility of a convex program with uncertain constraints gives a value for the maximal ‘size’ of an uncertainty set under which robust feasibility can be guaranteed. This paper provides an upper bound for the radius for convex programs with uncertain convex polynomial constraints and exact formulas for convex programs with SOS-convex polynomial constraints (or convex quadratic constraints) under affine data uncertainty. These exact formulas allow the radius to be comput...
Energy Technology Data Exchange (ETDEWEB)
Bevanger, K.; Bartzke, G.; Broeseth, H.; Gjershaug, J.O.; Hanssen, F.; Jacobsen, K.-O.; Kvaloey, P.; May, R.; Nygaard, T.; Pedersen, H.C.; Reitan, O.; Refsnaes, S.; Stokke, S.; Vang, R.
2009-12-15
From 2009 inclusive, NINA has received economic support for research on power lines and wildlife from the Norwegian Research Council (NFR) through the RENERGI Programme. The project is named 'Optimal design and routing of power lines; ecological, technical and economic perspectives' (OPTIPOL). It is scheduled for 5 years (2009-1013) and is part of the activities within CEDREN, i.e. the Centre for environmental design of renewable energy (cf. http://www.cedren.no). With a grid close to 200 000 km overhead power-lines, the associated rights-of-way (ROW) affect huge land areas in Norway. The overall goal is to develop predict-ing tools for optimal routing of power lines from an environmental perspective and assess technical and economic solutions to minimize conflicts with wildlife and habitat conservation. Thus, the OPTIPOL rationale is based on the belief that the negative effects of electricity transmission and distribution can be reduced with respect to birds and mammals. OPTIPOL has several ambitious objectives, and is divided into sub-projects and specific tasks. From the first of November a PhD-student became part of the project, a position that will be held for 4 years. The main objective of the PhD-activities will be to assess how and why different wildlife species use deforested areas below power lines, evaluate possible positive and negative effects of power-line ROWs, and assess the possibilities for quality improvement. Another part of the project is dedicated the effects of linear structures on movement patterns and distribution in the landscape in native deer species. Here we will examine how different spatial scales influence the processes that guide movement patterns, and responses to linear structures. Another focus will be small game species, with mountain hare, capercaillie, black grouse and hazel grouse as model species. The main objective will be to assess the impact of transforming ROW habitats into attractive small-game foraging
Decomposability of Abstract and Path-Induced Convexities in Hypergraphs
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Malvestuto Francesco Mario
2015-08-01
Full Text Available An abstract convexity space on a connected hypergraph H with vertex set V (H is a family C of subsets of V (H (to be called the convex sets of H such that: (i C contains the empty set and V (H, (ii C is closed under intersection, and (iii every set in C is connected in H. A convex set X of H is a minimal vertex convex separator of H if there exist two vertices of H that are separated by X and are not separated by any convex set that is a proper subset of X. A nonempty subset X of V (H is a cluster of H if in H every two vertices in X are not separated by any convex set. The cluster hypergraph of H is the hypergraph with vertex set V (H whose edges are the maximal clusters of H. A convexity space on H is called decomposable if it satisfies the following three properties:
Manly, Charles J; Chandrasekhar, Jayaraman; Ochterski, Joseph W; Hammer, Jack D; Warfield, Benjamin B
2008-02-01
The Hit-to-Lead-to-Candidate process continues to evolve rapidly, and while technological advances offer much potential, the reality often pales to the promise. Conversely, strategies and tactics implementing existing technologies may result in more benefit in the end. This article focuses on some of the thinking and approaches that may improve the efficiency and effectiveness of the beginnings of the drug discovery path. From the perspective of computational chemists, different types of strategy and philosophy of approach will be treated including: considerations of early lead choices, strategies for improving poor leads, multivariate optimization, opportunities for informatics, and engineering good decisions.
Bevanger, Kjetil Modolv; Bartzke, Gundula; Brøseth, Henrik; Dahl, Espen Lie; Gjershaug, Jan Ove; Hanssen, Frank Ole; Jacobsen, Karl Otto; Kleven, Oddmund; Kvaløy, Pål; May, Roelof Frans; Nygård, Torgeir; Refsnæs, Steinar; Stokke, Sigbjørn; Thomassen, Jørn; Meås, Roger
2014-01-01
Bevanger, K., Bartzke, G., Brøseth, H., Dahl, E.L., Gjershaug, J.O., Hanssen, F., Jacobsen, K.- O., Kleven, O., Kvaløy, P., May, R., Meås, R., Nygård, T., Refsnæs, S., Stokke, S. & Thomassen, J. 2014. Optimal design and routing of power lines; ecological, technical and economic perspectives (OPTIPOL). Final Report; findings 2009–2014. - NINA Report 1012. 92 pp. OPTIPOL was designed by NINA in early 2008, with a particular focus on power lines and wildlife interactions. As soon as ...
Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks
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Enming Dong
2014-01-01
Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.
Properties of distance functions on convex surfaces and Alexandrov spaces
Rataj, Jan
2009-01-01
If $X$ is a convex surface in a Euclidean space, then the squared (intrinsic) distance function $\\dist^2(x,y)$ is d.c. (DC, delta-convex) on $X\\times X$ in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of $\\dist^2(x,y)$ on $X \\times X$ if $X$ is an Alexandrov space with nonnegative curvature. Applications concerning $r$-boundaries (distance spheres) and the ambiguous locus (exoskeleton) of a closed subset of a convex surface are given.
Plane geometry and convexity of polynomial stability regions
Henrion, Didier
2008-01-01
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and Bezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.
Bubbles, convexity and the Black--Scholes equation
Ekström, Erik; 10.1214/08-AAP579
2009-01-01
A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in this paper we address some of these issues. In particular, we derive existence and uniqueness results for the Black--Scholes equation, and we provide convexity theory for option pricing and derive related ordering results with respect to volatility. We show that American options are convexity preserving, whereas European options preserve concavity for general payoffs and convexity only for bounded contracts.
Shape preserving rational cubic spline for positive and convex data
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Malik Zawwar Hussain
2011-11-01
Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.
Quadratic growth and stability in convex programming problems
Bonnans, J. Frederic; Ioffe, Alexander D.
1994-01-01
Projet PROMATH; Given a convex program with $C^2$ functions and a convex set $S$ of solutions to the problem, we give a second order condition which guarantees that the problem does not have solutions outside of $S$. This condition is interpreted as a characterization for the quadratic growth of the cost function. The crucial role in the proofs is played by a theorem describing a certain uniform regularity property of critical cones in smooth convex programs. We apply these results to the dis...
A Note on The Convexity of Chebyshev Sets
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Sangeeta
2009-07-01
Full Text Available Perhaps one of the major unsolved problem in Approximation Theoryis: Whether or not every Chebyshev subset of a Hilbert space must be convex. Many partial answers to this problem are available in the literature. R.R. Phelps[Proc. Amer. Math. Soc. 8 (1957, 790-797] showed that a Chebyshev set in an inner product space (or in a strictly convex normed linear space is convex if the associated metric projection is non-expansive. We extend this result to metricspaces.
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Yaping Hu
2015-01-01
the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.
Tarone, Elaine
2013-01-01
The topic of this "Perspectives" column is "Requiring a Proficiency Level as a Requirement for U.S. K-12 Teacher Licensure." In 1998, the American Council of Teachers of Foreign Languages (ACTFL) began to work with the National Council for Accreditation of Teacher Education (NCATE), which accredits teacher education programs…
Optimal design and routing of power lines; ecological, technical and economic perspectives (OPTIPOL)
Energy Technology Data Exchange (ETDEWEB)
Bevanger, K.; Bartzke, G.; Broeseth, H.; Gjershaug, J.O.; Hanssen, F.; Jacobsen, K.-O.; Kvaloey, P.; May, R.; Meaas, R.; Nygaard, T.; Refsnaes, S.; Stokke, S.; Vang, R.
2010-12-15
The OPTIPOL project - 'Optimal design and routing of power lines; ecological, technical and economic perspectives' - has been active for two years, although the main operational phase was delayed until autumn 2009. The overall OPTIPOL objective is to develop knowledge and tools to improve the decision on environmental friendly power-line routing. To achieve this goal the work is subdivided into 9 focal areas; Develop a 'least-cost path' GIS-based application for an environmental friendly routing of power lines based on ecological, financial and technological criteria; Assess habitat use of power-line Rights-of-Way (ROW) by different wildlife species, consider actions of improving power-line ROW as wildlife habitats, and evaluate possible positive and negative effects on wildlife of power-line ROWs. More specific we will examine how power-line ROW may offer suitable feeding grounds for moose and see if the species habitat selection is influenced by power line ROW; Assess population impact of bird mortality due to power-line collisions, relative to other human related mortality factors (primarily hunting) in gallinaceous birds (with capercaillie and black grouse as model species); Identify ecological high-risk factors for bird collisions, i.e. site-specific factors connected to topographic characteristics, including vegetation structure, season, weather and light conditions; Establish a national infrastructure for management of dead bird data (including birds re-corded as collision and electrocution victims) by developing an online web application enabling the general public to contribute with data on recorded dead birds via Internet; Review available literature to assess 1) the possibilities for increased collision hazard to birds by making power-line structures less visible for humans given the present knowledge on bird vision, and 2) technical properties and constraints of camouflaging techniques on conductors and earth wires; Review available
Flip to Regular Triangulation and Convex Hull.
Gao, Mingcen; Cao, Thanh-Tung; Tan, Tiow-Seng
2017-02-01
Flip is a simple and local operation to transform one triangulation to another. It makes changes only to some neighboring simplices, without considering any attribute or configuration global in nature to the triangulation. Thanks to this characteristic, several flips can be independently applied to different small, non-overlapping regions of one triangulation. Such operation is favored when designing algorithms for data-parallel, massively multithreaded hardware, such as the GPU. However, most existing flip algorithms are designed to be executed sequentially, and usually need some restrictions on the execution order of flips, making them hard to be adapted to parallel computation. In this paper, we present an in depth study of flip algorithms in low dimensions, with the emphasis on the flexibility of their execution order. In particular, we propose a series of provably correct flip algorithms for regular triangulation and convex hull in 2D and 3D, with implementations for both CPUs and GPUs. Our experiment shows that our GPU implementation for constructing these structures from a given point set achieves up to two orders of magnitude of speedup over other popular single-threaded CPU implementation of existing algorithms.
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
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.
CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
WU Zhiyou; ZHANG Liansheng; BAI Fusheng; YANG Xinmin
2004-01-01
In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function,then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem using the existing algorithms about them.
Directory of Open Access Journals (Sweden)
Fubin Pan
2015-09-01
Full Text Available Purpose: This paper is an attempt to establish the mathematical programming model of the vendor selection for the joint procurement from a total cost of ownership perspective. Design/methodology/approach: Fuzzy genetic algorithm is employed to solve the model, and the data set of the ball bearings purchasing problem is illustrated as a numerical analysis. Findings: According to the results, it can be seen that the performance of the optimization model is pretty good and can reduce the total costs of the procurement. Originality/value: The contribution of this paper is threefold. First, a literature review and classification of the published vendor selection models is shown in this paper. Second, a mathematical programming model of the vendor selection for the joint procurement from a total cost of ownership perspective is established. Third, an empirical study is displayed to illustrate the application of the proposed model to evaluate and identify the best vendors for ball bearing procurement, and the results show that it could reduce the total costs as much as twenty percent after the optimization.
Chen, Yifan; Zhou, Yu; Murch, Ross; Kosmas, Panagiotis
2017-04-01
To maximize the effect of treatment and minimize the adverse effect on patients, we propose to optimize nanorobots-assisted targeted drug delivery (TDD) for locoregional treatment of tumor from the perspective of touchable communication channel estimation and waveform design. The drug particles are the information molecules; the loading/injection and unloading of the drug correspond to the transmitting and receiving processes; the concentration-time profile of the drug particles administered corresponds to the signaling pulse. Given this analogy, we first propose to use contrast-enhanced microwave imaging (CMI) as a pretherapeutic evaluation technique to determine the pharmacokinetic model of nanorobots-assisted TDD. The CMI system applies an information-theoretic-criteria-based algorithm to estimate drug accumulation in tumor, which is analogous to the estimation of channel impulse response in the communication context. Subsequently, we present three strategies for optimal targeted therapies from the communication waveform design perspective, which are based on minimization of residual drug molecules at the end of each therapeutic session (i.e., inter-symbol interference), maximization of duration when the drug intensity is above a prespecified threshold during each therapeutic session (i.e., non-fade duration), and minimization of average rate that a therapeutic operation is not received correctly at tumor (i.e., bit error rate). Finally, numerical examples are applied to demonstrate the effectiveness of the proposed analytical framework.
Differential subordination for meromorphic multivalent quasi-convex functions
R. W. Ibrahim; M. Darus
2010-01-01
We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.
Differential subordination for meromorphic multivalent quasi-convex functions
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R. W. Ibrahim
2010-02-01
Full Text Available We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.
Lipschitz estimates for convex functions with respect to vector fields
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Valentino Magnani
2012-12-01
Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22].
Entropy and convexity for nonlinear partial differential equations.
Ball, John M; Chen, Gui-Qiang G
2013-12-28
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.
Subaperture Stitching Interferometry for Large Convex Aspheric Surfaces Project
National Aeronautics and Space Administration — The size and accuracy specifications of telescope mirrors are ever more demanding. This is particularly true for secondary mirrors, as they are convex and thus...
Two new definitions on convexity and related inequalities
Tunc, Mevlut
2012-01-01
We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt sense.
Pseudolinear functions and optimization
Mishra, Shashi Kant
2015-01-01
Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems.The book describes the characterizations of solution sets of various optimization problems. It examines multiobjective pseudolinear, multiobjective fractional pseudolinear, static minmax pseudolinear, and static minmax fractional pseudolinear optimization problems and their results. The authors extend these results to locally
Statistical Optimality in Multipartite Ranking and Ordinal Regression.
Uematsu, Kazuki; Lee, Yoonkyung
2015-05-01
Statistical optimality in multipartite ranking is investigated as an extension of bipartite ranking. We consider the optimality of ranking algorithms through minimization of the theoretical risk which combines pairwise ranking errors of ordinal categories with differential ranking costs. The extension shows that for a certain class of convex loss functions including exponential loss, the optimal ranking function can be represented as a ratio of weighted conditional probability of upper categories to lower categories, where the weights are given by the misranking costs. This result also bridges traditional ranking methods such as proportional odds model in statistics with various ranking algorithms in machine learning. Further, the analysis of multipartite ranking with different costs provides a new perspective on non-smooth list-wise ranking measures such as the discounted cumulative gain and preference learning. We illustrate our findings with simulation study and real data analysis.
Continuity of Extremal Elements in Uniformly Convex Spaces
Ferguson, Timothy
2013-01-01
In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, we simplify and clarify Ryabykh's proof that for any linear functional on a uniformly convex Bergman space with kernel in a certain Hardy space, the extremal functional belongs to the corresponding Hardy space.
Convex games, clan games, and their marginal games
Branzei , Rodica; Dimitrov, Dinko; Tijs, Stef
2005-01-01
We provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. As it turns out, a cooperative game is convex if and only if all its marginal games are superadditive, and a monotonic game satisfying the veto player property with respect to the members of a coalition C is a total clan game (with clan C) if and only if all its C-based marginal games are subadditive.
Hunt, Jeffrey; Barrett, Rowland; Grapentine, W. Lex; Liguori, Gina; Trivedi, Harsh K.
2008-01-01
Objectives: The ability to develop quality medical student exposures in child and adolescent psychiatry is critical to the professional development of these future physicians and to the growth of recruitment efforts into the field. This study identifies teaching perspectives among child and adolescent psychiatry faculty to determine whether there…
Hunt, Jeffrey; Barrett, Rowland; Grapentine, W. Lex; Liguori, Gina; Trivedi, Harsh K.
2008-01-01
Objectives: The ability to develop quality medical student exposures in child and adolescent psychiatry is critical to the professional development of these future physicians and to the growth of recruitment efforts into the field. This study identifies teaching perspectives among child and adolescent psychiatry faculty to determine whether there…
Convex Aspherical Surface Testing Using Catadioptric Partial Compensating System
Wang, Jingxian; Hao, Qun; Hu, Yao; Wang, Shaopu; Li, Tengfei; Tian, Yuhan; Li, Lin
2016-01-01
Aspheric optical components are the indispensable part of modern optics systems. With the constant development of aspheric optical fabrication technique, the systems with large aperture convex aspheric optical components are widely used in astronomy and space optics. Thus, the measurement of the figure error of the whole convex aspherical surface with high precision comes to be a challenge in the area of optical surface manufacture, and surface testing method is also very important. This paper presents a new partial compensating system by the combination of a refractive lens and a reflective mirror for testing convex aspherical surface. The refractive lens is used to compensate the aberration of the tested convex asphere partially. The reflective mirror is a spherical mirror which is coaxial to the refractive lens and reflecting the lights reflected by the tested convex asphere back to the convex asphere itself. With the long focal length and large aperture system we can realize a lighter and more compact system than the refractive partial compensating system because the spheric reflective mirror is more easily to realize and can bending the light conveniently.
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Xiaomin Xu
2016-07-01
Full Text Available With the rapid development of renewable energy, power supply structure is changing. However, thermal power is still dominant. With the background in low carbon economy, reasonable adjustment and optimization of the power supply structure is the trend of future development in the power industry. It is also a reliable guarantee of a fast, healthy and stable development of national economy. In this paper, the sustainable development of renewable energy sources is analyzed from the perspective of power supply. Through the research on the development of power supply structure, we find that regional power supply structure development mode conforms to dynamic characteristics and there must exist a Markov chain in the final equilibrium state. Combined with the characteristics of no aftereffect and small samples, this paper applies a Markov model to the power supply structure prediction. The optimization model is established to ensure that the model can fit the historical data as much as possible. Taking actual data of a certain area of Ningxia Province as an example, the models proposed in this paper are applied to the practice and results verify the validity and robustness of the model, which can provide decision basis for enterprise managers.
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Rafa Espínola
2010-01-01
Full Text Available We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
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Horváth László
2011-01-01
Full Text Available Abstract In this paper, a new parameter-dependent refinement of the discrete Jensen's inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem with probability theoretical background. We apply the results to define some new quasi-arithmetic and mixed symmetric means and study their monotonicity and convergence.
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-hu; YAN Wen-jun; LU Jian-ning; ZHAO Guang-zhou
2005-01-01
Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl2 and GH2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system.Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results,multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.
Zhang, Yunong; Wang, Jun
2002-06-01
A recurrent neural network called the dual neural network is proposed in this Letter for solving the strictly convex quadratic programming problems. Compared to other recurrent neural networks, the proposed dual network with fewer neurons can solve quadratic programming problems subject to equality, inequality, and bound constraints. The dual neural network is shown to be globally exponentially convergent to optimal solutions of quadratic programming problems. In addition, compared to neural networks containing high-order nonlinear terms, the dynamic equation of the proposed dual neural network is piecewise linear, and the network architecture is thus much simpler. The global convergence behavior of the dual neural network is demonstrated by an illustrative numerical example.
DEFF Research Database (Denmark)
Kussmann, Martin; Morine, Melissa J; Hager, Jörg
2013-01-01
We review here the status of human type 2 diabetes studies from a genetic, epidemiological, and clinical (intervention) perspective. Most studies limit analyses to one or a few omic technologies providing data of components of physiological processes. Since all chronic diseases are multifactorial...... of the complexity of T2DM, we propose a systems biology approach to advance the understanding of origin, onset, development, prevention, and treatment of this complex disease. This systems-based strategy is based on new study design principles and the integrated application of omics technologies: we pursue...
L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing
Demetriou, I. C.
2006-04-01
Fortran 77 software is given for least squares smoothing to data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is also unknown of the optimization problem. A highly useful description of the constraints is that they follow from the assumption of initially increasing and subsequently decreasing rates of change, or vice versa, of the process considered. The underlying algorithm partitions the data into two disjoint sets of adjacent data and calculates the required fit by solving a strictly convex quadratic programming problem for each set. The piecewise linear interpolant to the fit is convex on the first set and concave on the other one. The partition into suitable sets is achieved by a finite iterative algorithm, which is made quite efficient because of the interactions of the quadratic programming problems on consecutive data. The algorithm obtains the solution by employing no more quadratic programming calculations over subranges of data than twice the number of the divided differences constraints. The quadratic programming technique makes use of active sets and takes advantage of a B-spline representation of the smoothed values that allows some efficient updating procedures. The entire code required to implement the method is 2920 Fortran lines. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes over subranges of data that is only proportional to the number of data. The results suggest that the package can be used for very large numbers of data values. Some examples with output are provided to help new users and exhibit certain features of the software. Important applications of the smoothing technique may be found in calculating a sigmoid approximation, which is a common topic in various contexts in applications in disciplines like physics, economics
The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities
Cain, George L., Jr.; González, Luis
2008-02-01
The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.
Carver, Charles S.; Scheier, Michael F.; Segerstrom, Suzanne C.
2010-01-01
Optimism is an individual difference variable that reflects the extent to which people hold generalized favorable expectancies for their future. Higher levels of optimism have been related prospectively to better subjective well-being in times of adversity or difficulty (i.e., controlling for previous well-being). Consistent with such findings, optimism has been linked to higher levels of engagement coping and lower levels of avoidance, or disengagement, coping. There is evidence that optimism is associated with taking proactive steps to protect one's health, whereas pessimism is associated with health-damaging behaviors. Consistent with such findings, optimism is also related to indicators of better physical health. The energetic, task-focused approach that optimists take to goals also relates to benefits in the socioeconomic world. Some evidence suggests that optimism relates to more persistence in educational efforts and to higher later income. Optimists also appear to fare better than pessimists in relationships. Although there are instances in which optimism fails to convey an advantage, and instances in which it may convey a disadvantage, those instances are relatively rare. In sum, the behavioral patterns of optimists appear to provide models of living for others to learn from. PMID:20170998
Betta, Monica; Laurino, Marco; Pugliese, Andrea; Guzzetta, Giorgio; Landi, Alberto; Manfredi, Piero
2016-03-16
Herpes zoster arises from reactivation of the varicella-zoster virus (VZV), causing varicella in children. As reactivation occurs when cell-mediated immunity (CMI) declines, and there is evidence that re-exposure to VZV boosts CMI, mass varicella immunization might increase the zoster burden, at least for some decades. Fear of this natural zoster boom is the main reason for the paralysis of varicella immunization in Europe. We apply optimal control to a realistically parametrized age-structured model for VZV transmission and reactivation to investigate whether feasible varicella immunization paths that are optimal in controlling both varicella and zoster exist. We analyse the optimality system numerically focusing on the role of the cost functional, of the relative zoster-varicella cost and of the planning horizon length. We show that optimal programmes will mostly be unfeasible for public health owing to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programmes when aiming to control both varicella and zoster. However, we show that gradually increasing-hence feasible-vaccination schedules can perform better than routine programmes with constant vaccine uptake. Finally, we show the optimal profiles of feasible programmes targeting mitigation of the post-immunization natural zoster boom with priority.
Using convex quadratic programming to model random media with Gaussian random fields
Quintanilla, John A.; Jones, W. Max
2007-04-01
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented
Social influence makes self-interested crowds smarter: an optimal control perspective
Luo, Yu; Venkatasubramanian, Venkat
2016-01-01
It is very common to observe crowds of individuals solving similar problems with similar information in a largely independent manner. We argue here that crowds can become "smarter," i.e., more efficient and robust, by partially following the average opinion. This observation runs counter to the widely accepted claim that the wisdom of crowds deteriorates with social influence. The key difference is that individuals are self-interested and hence will reject feedbacks that do not improve their performance. We propose a control-theoretic methodology to compute the degree of social influence, i.e., the level to which one accepts the population feedback, that optimizes performance. We conducted an experiment with human subjects ($N = 194$), where the participants were first asked to solve an optimization problem independently, i.e., under no social influence. Our theoretical methodology estimates a $30\\%$ degree of social influence to be optimal, resulting in a $29\\%$ improvement in the crowd's performance. We the...
Preventive Maintenance Optimization in Healthcare Domain: Status of Research and Perspective
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H. Mahfoud
2016-01-01
Full Text Available Although medical equipment maintenance has been carefully managed for years, very few in-depth studies have been conducted to evaluate the effectiveness and efficiency of these implemented preventive maintenance strategies, especially after the debate about the credibility of manufacturer’s recommendations has increased in the clinical engineering community. Facing the dilemma of merely following manufactures maintenance manual or establishing an evidence-based maintenance, medical equipment maintenance could have exploited an advanced area in operations research which is maintenance optimization research. In this paper, we review and examine carefully the status of application oriented research on preventive maintenance optimization of medical devices. This study addresses preventive healthcare maintenance with a focus on factors influencing the maintenance decision making. The analysis is structured by defining different aspects necessary to construct a maintenance optimization model. We conclusively propose directions to develop suitable tools for better healthcare maintenance management.
A Posteriori Equivalence: A New Perspective for Design of Optimal Channel Shortening Equalizers
Venkataramani, Raman
2007-01-01
The problem of channel shortening equalization for optimal detection in ISI channels is considered. The problem is to choose a linear equalizer and a partial response target filter such that the combination produces the best detection performance. Instead of using the traditional approach of MMSE equalization, we directly seek all equalizer and target pairs that yield optimal detection performance in terms of the sequence or symbol error rate. This leads to a new notion of a posteriori equivalence between the equalized and target channels with a simple characterization in terms of their underlying probability distributions. Using this characterization we show the surprising existence an infinite family of equalizer and target pairs for which any maximum a posteriori (MAP) based detector designed for the target channel is simultaneously MAP optimal for the equalized channel. For channels whose input symbols have equal energy, such as q-PSK, the MMSE equalizer designed with a monic target constraint yields a so...
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Herman van Wietmarschen
2017-05-01
Full Text Available Western science has been strong in measuring details of biological systems such as gene expression levels and metabolite concentrations, and has generally followed a bottom up approach with regard to explaining biological phenomena. Chinese medicine in contrast has evolved as a top down approach in which body and mind is seen as a whole, a phenomenological approach based on the organization and dynamics of symptom patterns. Western and Chinese perspectives are developing towards a ‘middle out’ approach. Chinese medicine diagnosis, we will argue, allows bridging the gap between biologists and psychologists and offers new opportunities for the development of health monitoring tools and health promotion strategies.
Characterizing optimism and pessimism directly though comonotonicity
Wakker, P.
1990-01-01
Schmeidler (1982) introduced comonotonic independence to characterize nonadditivity of probabilities. This note obtains natural and very simple characterizations of convexity, concavity (and additivity) of nonadditive probabilities, by relating these directly to the pessimism and optimism inherent
Institute of Scientific and Technical Information of China (English)
XIAO Rui-Zhu
2014-01-01
Transliteration aims to adapt loanwords to perfect sound patterns and structures. With the guidance of Optimality The-ory, this paper elaborates on the constraints that must be observed in transliteration to achieve Chinese phonological harmony from phonemic equivalents. It analyzes the ranking of constraints for structural acceptability of the loanwords.
Institute of Scientific and Technical Information of China (English)
肖瑞珠
2014-01-01
Transliteration aims to adapt loanwords to perfect sound patterns and structures. With the guidance of Optimality Theory, this paper elaborates on the constraints that must be observed in transliteration to achieve Chinese phonological harmony from phonological structure. It analyzes the ranking of constraints for structural acceptability of the loanwords.
Current perspectives on the optimal age to spay/castrate dogs and cats
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Howe LM
2015-05-01
Full Text Available Lisa M HoweDepartment of Small Animal Clinical Sciences, College of Veterinary Medicine and Biomedical Sciences, Texas A&M University, College Station, TX, USAAbstract: Spaying and castrating of dogs and cats has been considered for decades to be a routine standard of practice in veterinary medicine in the US for the prevention of numerous undesirable behaviors, medical conditions, and diseases. Additionally, the procedures have been promoted as a method of curbing the severe pet-overpopulation problem in the US. Recently, however, this routine practice has come under scrutiny and become a very controversial topic. The general wisdom and safety of the procedures have been questioned by those who are concerned that the procedures may have some unintended consequences that are only recently being recognized. The purpose of this paper is to critically examine the scientific literature regarding elective spay/castration procedures and present both risks and benefits of elective gonadectomy. After the literature is examined, it becomes clear that there may not be a single absolute optimal age to spay or castrate all dogs and cats, but that the optimal age may be dependent upon several factors, including species, breed, body size, and breed-specific diseases, among others. Determining the optimal age to perform elective gonadectomy is much clearer in cats, and the literature demonstrates that the procedures can typically be safely performed at any age after 6–8 weeks of age. The optimal age to spay or castrate dogs of certain breeds (rottweiler, golden retriever, Labrador retriever, and vizsla is becoming less clear as studies are being conducted as to the health benefits and risks in those breeds. This review will examine these controversies and make recommendations as to the optimal age to spay/castrate dogs based upon the scientific literature.Keywords: gonadectomy (neuter, ovariohysterectomy (spay, castration, neoplasia, longevity, orthopedic
Smooth Optimization Approach for Sparse Covariance Selection
Lu, Zhaosong
2009-01-01
In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply Nesterov's smooth optimization technique [Y.E. Nesterov, Dokl. Akad. Nauk SSSR, 269 (1983), pp. 543--547; Y. E. Nesterov, Math. Programming, 103 (2005), pp. 127--152] to their dual counterparts that are smooth convex problems. It is shown that the resulting approach...
Duality without constraint qualification in nonsmooth optimization
S. Nobakhtian
2006-01-01
We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality res...
Cavitation bubbles collapse characteristics behind a convex body
Institute of Scientific and Technical Information of China (English)
李瑶; 许唯临; 张亚磊; 张敬威; 陈春祺; 阿蓉
2013-01-01
Cavitation bubbles behind a convex body were experimentally studied by a high speed camera and a hydrophone synch- ronously. The experiments were conducted in a circulating water tunnel with five various contraction ratios:b=0.497,b=0.6,b=0.697,b=0.751, andb=0.799. The distributions of the cavitation bubble collapse positions behind the five different convex bodies were obtained by combining the images taken by the high speed camera. According to the collapse positions, it was found that no cavitation bubble was collapsed in the region near the wall until the ratio of the water head loss over the convex body height was larger than 20, which can be used to predict if the cavitation damage would occur in the tunnel with orifice energy dissipaters.
Trace-Inequalities and Matrix-Convex Functions
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Tsuyoshi Ando
2010-01-01
Full Text Available A real-valued continuous function f(t on an interval (α,β gives rise to a map X↦f(X via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: Tr(f(B−f(A(C−B≤Tr(f(C−f(B(B−A for A≤B≤C. A related topic will be also discussed.
RESEARCH ANNOUNCEMENTS Helly Type Problems for Some Special Convex Polygons
Institute of Scientific and Technical Information of China (English)
苑立平; 丁仁
2001-01-01
@@In the combinatorial geometry of convex sets the question of how efficiently a family of convex sets can be pierced by points has led to various problems which may be regarded as extensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviated as Пn) if there exists a set of n points such that each member of the family contains at least one of them. A family of sets is said to be Пnk if every subfamily of size k or less is Пn. The famous Helly theorem in combinatorial geometry asserts that for finite families of convex sets in the plane П13 implies П1. In a recent paper by M. Katchalski and D. Nashtir[a] the following conjecture of Griinbaum[2] was mentioned again:
Widths of some classes of convex functions and bodies
Konovalov, V. N.; Maiorov, Vitalii E.
2010-02-01
We consider classes of uniformly bounded convex functions defined on convex compact bodies in \\mathbb{R}^d and satisfying a Lipschitz condition and establish the exact orders of their Kolmogorov, entropy, and pseudo-dimension widths in the L_1-metric. We also introduce the notions of pseudo-dimension and pseudo-dimension widths for classes of sets and determine the exact orders of the entropy and pseudo-dimension widths of some classes of convex bodies in \\mathbb{R}^drelative to the pseudo-metric defined as the d-dimensional Lebesgue volume of the symmetric difference of two sets. We also find the exact orders of the entropy and pseudo-dimension widths of the corresponding classes of characteristic functions in L_p-spaces, 1\\le p\\le\\infty.
Convex minorants of random walks and L\\'evy processes
Abramson, Josh; Ross, Nathan; Bravo, Gerónimo Uribe
2011-01-01
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and L\\'evy processes which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and L\\'evy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.
Small sets in convex geometry and formal independence over ZFC
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Menachem Kojman
2005-01-01
Full Text Available To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets (S which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations.
Dose evaluation from multiple detector outputs using convex optimisation.
Hashimoto, Makoto; Iimoto, Takeshi; Kosako, Toshiso
2011-07-01
A dose evaluation using multiple radiation detectors can be improved by the convex optimisation method. It enables flexible dose evaluation corresponding to the actual radiation energy spectrum. An application to the neutron ambient dose equivalent evaluation is investigated using a mixed-gas proportional counter. The convex derives the certain neutron ambient dose with certain width corresponding to the true neutron energy spectrum. The range of the evaluated dose is comparable to the error of conventional neutron dose measurement equipments. An application to the neutron individual dose equivalent measurement is also investigated. Convexes of particular dosemeter combinations evaluate the individual dose equivalent better than the dose evaluation of a single dosemeter. The combinations of dosemeters with high orthogonality of their response characteristics tend to provide a good suitability for dose evaluation.
Polyominoes with nearly convex columns: A model with semidirected blocks
Feretic, Svjetlan
2009-01-01
In most of today's exactly solved classes of polyominoes, either all members are convex (in some way), or all members are directed, or both. If the class is neither convex nor directed, the exact solution uses to be elusive. This paper is focused on polyominoes with hexagonal cells. Concretely, we deal with polyominoes whose columns can have either one or two connected components. Those polyominoes (unlike the well-explored column-convex polyominoes) cannot be exactly enumerated by any of the now existing methods. It is therefore appropriate to introduce additional restrictions, thus obtaining solvable subclasses. In our recent paper, published in this same journal, the restrictions just mentioned were semidirectedness and an upper bound on the size of the gap within a column. In this paper, the semidirectedness requirement is made looser. The result is that now the exactly solved subclasses are larger and have greater growth constants. These new polyomino families also have the advantage of being invariant u...
AN EFFICIENT ALGORITHM FOR THE CONVEX HULL OF PLANAR SCATTERED POINT SET
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Z. Fu
2012-07-01
Full Text Available Computing the convex hull of a point set is requirement in the GIS applications. This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set. It adopts approach that dividing the point set into several sub regions to get an initial convex hull boundary firstly. Then the points on the boundary, which cannot be vertices of the minimum convex hull, are removed one by one. Finally the concave points on the boundary, which cannot be vertices of the minimum convex hull, are withdrew. Experimental analysis shows the efficiency of the algorithm compared with other methods.
Investigating the optimal soy protein and isoflavone intakes for women: a perspective.
Messina, Mark
2008-07-01
Traditional soyfoods have been consumed for centuries throughout much of East Asia and, recently, these foods have also become popular in the West. Soyfoods and specific soybean components, such as the protein and isoflavones, have attracted attention for their possible health benefits. Isoflavones are classified as phytoestrogens and have been postulated to be natural alternatives to hormone therapy for menopausal women. To provide guidance on optimal soy intake, this article evaluates Asian soy consumption and both clinical and Asian epidemiologic studies that examined the relationship between soy intake and a variety of health outcomes. On the basis of these data and the standard principles of dietary practice the author suggests that optimal soy protein and isoflavone intakes are 15-20 g/day and 50-90 mg/day, respectively. In addition, an intake of 25 g/day soy protein can be specifically used as the recommendation for cholesterol reduction.
Nonparametric estimation of a convex bathtub-shaped hazard function.
Jankowski, Hanna K; Wellner, Jon A
2009-11-01
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.
Convex Four Body Central Configurations with Some Equal Masses
Perez-Chavela, Ernest
2009-01-01
We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such central configuration posses a symmetry line and it is a kite shaped quadrilateral. We also show that there is exactly one convex non-collinear central configuration when the opposite masses are equal. Such central configuration also posses a symmetry line and it is a rhombus.
Finding Convex Hulls Using Quickhull on the GPU
Tzeng, Stanley
2012-01-01
We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of problems. Our framework transforms the recursive splitting step into a permutation step that is well-suited for graphics hardware. Our convex hull algorithm of choice is Quickhull. Our parallel Quickhull implementation (for both 2D and 3D cases) achieves an order of magnitude speedup over standard computational geometry libraries.
Convexity and the "Pythagorean" metric of space(-time)
Kalogeropoulos, Nikos
2016-01-01
We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2013-08-01
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.
Convex Combination of Multiple Statistical Models with Application to VAD
DEFF Research Database (Denmark)
Petsatodis, Theodoros; Boukis, Christos; Talantzis, Fotios
2011-01-01
This paper proposes a robust Voice Activity Detector (VAD) based on the observation that the distribution of speech captured with far-field microphones is highly varying, depending on the noise and reverberation conditions. The proposed VAD employs a convex combination scheme comprising three...... statistical distributions - a Gaussian, a Laplacian, and a two-sided Gamma - to effectively model captured speech. This scheme shows increased ability to adapt to dynamic acoustic environments. The contribution of each distribution to this convex combination is automatically adjusted based on the statistical...
Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function
Seijo, Emilio
2010-01-01
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided. We also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization, computation and consistency of its least squares estimator.
Optimal Reinsurance Design for Pareto Optimum: From the Perspective of Multiple Reinsurers
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Xing Rong
2016-01-01
Full Text Available This paper investigates optimal reinsurance strategies for an insurer which cedes the insured risk to multiple reinsurers. Assume that the insurer and every reinsurer apply the coherent risk measures. Then, we find out the necessary and sufficient conditions for the reinsurance market to achieve Pareto optimum; that is, every ceded-loss function and the retention function are in the form of “multiple layers reinsurance.”
On the Optimization of the IEEE 802.11 DCF: A Cross-Layer Perspective
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Massimiliano Laddomada
2010-01-01
Full Text Available This paper is focused on the problem of optimizing the aggregate throughput of the distributed coordination function (DCF employing the basic access mechanism at the data link layer of IEEE 802.11 protocols. We consider general operating conditions accounting for both nonsaturated and saturated traffic in the presence of transmission channel errors, as exemplified by the packet error rate . The main clue of this work stems from the relation that links the aggregate throughput of the network to the packet rate of the contending stations. In particular, we show that the aggregate throughput ( presents two clearly distinct operating regions that depend on the actual value of the packet rate with respect to a critical value , theoretically derived in this work. The behavior of ( paves the way to a cross-layer optimization algorithm, which proved to be effective for maximizing the aggregate throughput in a variety of network operating conditions. A nice consequence of the proposed optimization framework relies on the fact that the aggregate throughput can be predicted quite accurately with a simple, yet effective, closed-form expression. Finally, theoretical and simulation results are presented in order to unveil, as well as verify, the key ideas.
Directory of Open Access Journals (Sweden)
Haichao Wang
2017-07-01
Full Text Available A district heating (DH system is one of the most important components of infrastructures in cold areas. Proper DH network design should balance the initial investment and the heat distribution cost of the DH network. Currently, this design is often based on a recommended value for specific pressure loss (R = ∆P/L in the main lines. This will result in a feasible network design, but probably not be optimal in most cases. The paper develops a novel optimization model to facilitate the design by considering the initial investment in the pipes and the heat distribution costs. The model will generate all possible network scenarios consisting of different series of diameters for each pipe in the flow direction of the network. Then, the annuity on the initial investment, the heat distribution cost, and the total annual cost will be calculated for each network scenario, taking into account the uncertainties of the material prices and the yearly operating time levels. The model is applied to a sample DH network and the results indicate that the model works quite well, clearly identifying the optimal network design and demonstrating that the heat distribution cost is more important than the initial investment in DH network design.
Wind turbine pitch optimization
DEFF Research Database (Denmark)
Biegel, Benjamin; Juelsgaard, Morten; Stoustrup, Jakob
2011-01-01
for maximizing power production while simultaneously minimizing fatigue loads. In this paper, we show how this problem can be approximately solved using convex optimization. When there is full knowledge of the wind field, numerical simulations show that force and torque RMS variation can be reduced by over 96...
Non-convex polygons clustering algorithm
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Kruglikov Alexey
2016-01-01
Full Text Available A clustering algorithm is proposed, to be used as a preliminary step in motion planning. It is tightly coupled to the applied problem statement, i.e. uses parameters meaningful only with respect to it. Use of geometrical properties for polygons clustering allows for a better calculation time as opposed to general-purpose algorithms. A special form of map optimized for quick motion planning is constructed as a result.
Wu, Ruidong; Long, Yongcheng; Malanson, George P; Garber, Paul A; Zhang, Shuang; Li, Diqiang; Zhao, Peng; Wang, Longzhu; Duo, Hairui
2014-01-01
By addressing several key features overlooked in previous studies, i.e. human disturbance, integration of ecosystem- and species-level conservation features, and principles of complementarity and representativeness, we present the first national-scale systematic conservation planning for China to determine the optimized spatial priorities for biodiversity conservation. We compiled a spatial database on the distributions of ecosystem- and species-level conservation features, and modeled a human disturbance index (HDI) by aggregating information using several socioeconomic proxies. We ran Marxan with two scenarios (HDI-ignored and HDI-considered) to investigate the effects of human disturbance, and explored the geographic patterns of the optimized spatial conservation priorities. Compared to when HDI was ignored, the HDI-considered scenario resulted in (1) a marked reduction (∼9%) in the total HDI score and a slight increase (∼7%) in the total area of the portfolio of priority units, (2) a significant increase (∼43%) in the total irreplaceable area and (3) more irreplaceable units being identified in almost all environmental zones and highly-disturbed provinces. Thus the inclusion of human disturbance is essential for cost-effective priority-setting. Attention should be targeted to the areas that are characterized as moderately-disturbed, spatially optimized national-scale portfolio of conservation priorities--effectively representing the overall biodiversity of China while minimizing conflicts with economic development. Our results offer critical insights for current conservation and strategic land-use planning in China. The approach is transferable and easy to implement by end-users, and applicable for national- and local-scale systematic conservation prioritization practices.
Generalized concavity in fuzzy optimization and decision analysis
Ramík, Jaroslav
2002-01-01
Convexity of sets in linear spaces, and concavity and convexity of functions, lie at the root of beautiful theoretical results that are at the same time extremely useful in the analysis and solution of optimization problems, including problems of either single objective or multiple objectives. Not all of these results rely necessarily on convexity and concavity; some of the results can guarantee that each local optimum is also a global optimum, giving these methods broader application to a wider class of problems. Hence, the focus of the first part of the book is concerned with several types of generalized convex sets and generalized concave functions. In addition to their applicability to nonconvex optimization, these convex sets and generalized concave functions are used in the book's second part, where decision-making and optimization problems under uncertainty are investigated. Uncertainty in the problem data often cannot be avoided when dealing with practical problems. Errors occur in real-world data for...
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints. Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.
QR Code Image Correction based on Corner Detection and Convex Hull Algorithm
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Suran Kong
2013-12-01
Full Text Available Since the angular deviation produced when shooting a QR code image by a camera would cause geometric distortion of the QR code image, the traditional algorithm of QR code image correction would produce distortion. Therefore this paper puts forward the algorithm which combines corner detection with convex hull algorithm. Firstly, binaryzation of the collected QR code image with uneven light is obtained by the methods of local threshold and mathematical morphology. Next, the outline of the QR code and the dots on it are found and the distorted image is recovered by perspective collineation, according to the algorithm raised by this paper. Finally, experimental verification is made that the algorithm raised by this paper can correctly find the four apexes of QR code and achieves good effects of geometric correction. It will also significantly increase the recognition rate of seriously distorted QR code images
Duality in vector optimization
Bot, Radu Ioan
2009-01-01
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the s
Avis, D; Ito, T; Avis, David; Imai, Hiroshi; Ito, Tsuyoshi
2006-01-01
In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the pap...
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
Piñeros, William D.; Baldea, Michael; Truskett, Thomas M.
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Synthesis of a robust broadband duct ANC system using convex programming approach
Bai, Mingsian R.; Zeung, Pingshun
2002-04-01
A robust active controller using spatially feedforward structure is proposed for broadband attenuation of noise in ducts. To meet the requirements of performance and robust stability in the presence of plant uncertainties, an H2 cost function and an H∞ constrain are employed in the synthesis of the controller. The design is then converted into a convex programming problem using Q-parametrization and frequency discretization. An optimal controller that satisfies the quadratic cost functions and linear inequality constraints can be found by sequential quadratic programming. The optimal controller was implemented via a digital signal processor (DSP) and verified by experiments. Experiment results showed that the system attained 16.5 dB maximal attenuation and 5.9 dB total attenuation in the frequency band 200-600 Hz.
A novel neural dynamical approach to convex quadratic program and its efficient applications.
Xia, Youshen; Sun, Changyin
2009-12-01
This paper proposes a novel neural dynamical approach to a class of convex quadratic programming problems where the number of variables is larger than the number of equality constraints. The proposed continuous-time and proposed discrete-time neural dynamical approach are guaranteed to be globally convergent to an optimal solution. Moreover, the number of its neurons is equal to the number of equality constraints. In contrast, the number of neurons in existing neural dynamical methods is at least the number of the variables. Therefore, the proposed neural dynamical approach has a low computational complexity. Compared with conventional numerical optimization methods, the proposed discrete-time neural dynamical approach reduces multiplication operation per iteration and has a large computational step length. Computational examples and two efficient applications to signal processing and robot control further confirm the good performance of the proposed approach.
User and clinician perspectives on DEKA arm: results of VA study to optimize DEKA arm.
Resnik, Linda; Klinger, Shana Lieberman; Etter, Katherine
2014-01-01
This article summarizes feedback from Department of Veterans Affairs (VA) subjects and clinicians gathered during the VA optimization study of the DEKA Arm. VA subjects and clinicians tested two DEKA Arm prototypes (second-generation [gen 2] and third-generation [gen 3]). Features of the prototypes in three configurations are described. DEKA used feedback from the VA optimization study and from their own subjects to refine the gen 2 prototype. Thirty-three unique subjects participated in the VA evaluation; 26 participated in the gen 2 evaluation (1 subject participated twice), 13 participated in the gen 3 evaluation, and 5 participated in both gen 2 and gen 3 evaluations. Subject data were gathered through structured and open-ended surveys, interviews, and audio- and videotaped sessions. Study prosthetists and therapists provided ongoing feedback and completed surveys at the end of each subject's protocol. Eleven categories of feedback were identified: weight, cosmesis, hand grips, wrist design, elbow design, end-point control, foot controls, batteries and chargers, visual notifications, tactor, and socket features. Final feedback on the gen 3 was generally positive, particularly regarding improvements in wrist design, visual notifications, foot controls, end-point control, and cosmesis. Additional refinements to make the device lighter in weight, eliminate external wires and cables, and eliminate the external battery may further enhance its perceived usability and acceptability.
A capacity scaling algorithm for convex cost submodular flows
Energy Technology Data Exchange (ETDEWEB)
Iwata, Satoru [Kyoto Univ. (Japan)
1996-12-31
This paper presents a scaling scheme for submodular functions. A small but strictly submodular function is added before scaling so that the resulting functions should be submodular. This scaling scheme leads to a weakly polynomial algorithm to solve minimum cost integral submodular flow problems with separable convex cost functions, provided that an oracle for exchange capacities are available.
Bounds for Minkowski Billiard Trajectories in Convex Bodies
Artstein-Avidan, Shiri
2011-01-01
In this paper we use the Ekeland-Hofer-Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in ${\\mathbb R}^{n}$. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.
Schur convexity for a class of symmetric functions
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.
Method for solving a convex integer programming problem
Stefanov, Stefan M.
2003-01-01
We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.
ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE
Institute of Scientific and Technical Information of China (English)
Yang Changsen; Wang Fenghui
2007-01-01
In this article, the authors study a generalized modulus of convexity, δ(α)(∈).Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ∈, 0 ≤∈≤1, such that δ(α)(1 + ∈) ＞ (1 - α)∈.
Bounded cohomology with coefficients in uniformly convex Banach spaces
Bestvina, Mladen; Bromberg, Ken; Fujiwara, Koji
2013-01-01
We show that for acylindrically hyperbolic groups $\\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\\rho$ of $\\Gamma$ in a (nonzero) uniformly convex Banach space the vector space $H^2_b(\\Gamma;\\rho)$ is infinite dimensional. The result was known for the regular representations on $\\ell^p(\\Gamma)$ with $1
Systematization of problems on ball estimates of a convex compactum
Dudov, S. I.
2015-09-01
We consider a class of finite-dimensional problems on the estimation of a convex compactum by a ball of an arbitrary norm in the form of extremal problems whose goal function is expressed via the function of the distance to the farthest point of the compactum and the function of the distance to the nearest point of the compactum or its complement. Special attention is devoted to the problem of estimating (approximating) a convex compactum by a ball of fixed radius in the Hausdorff metric. It is proved that this problem plays the role of the canonical problem: solutions of any problem in the class under consideration can be expressed via solutions of this problem for certain values of the radius. Based on studying and using the properties of solutions of this canonical problem, we obtain ranges of values of the radius in which the canonical problem expresses solutions of the problems on inscribed and circumscribed balls, the problem of uniform estimate by a ball in the Hausdorff metric, the problem of asphericity of a convex body, the problems of spherical shells of the least thickness and of the least volume for the boundary of a convex body. This makes it possible to arrange the problems in increasing order of the corresponding values of the radius. Bibliography: 34 titles.
Intracranial Convexity Lipoma with Massive Calcification: Case Report
Energy Technology Data Exchange (ETDEWEB)
Kim, Eung Tae; Park, Dong Woo; Ryu, Jeong Ah; Park, Choong Ki; Lee, Young Jun; Lee, Seung Ro [Dept. of Radiology, Hanyang University College of Medicine, Seoul (Korea, Republic of)
2011-12-15
Intracranial lipoma is a rare entity, accounting for less than 0.5% of intracranial tumors, which usually develops in the callosal cisterns. We report a case of lipoma with an unusual location; in the high parietal convexity combined with massive calcification, and no underlying vascular malformation or congenital anomaly.
On a convex combination of solutions to elliptic variational inequalities
Directory of Open Access Journals (Sweden)
Sergiu Aizicovici
2007-02-01
Full Text Available We consider continuous descent methods for the minimization of convex functions defined on a general Banach space. In our previous work we showed that most of them (in the sense of Baire category converged. In the present paper we show that convergent continuous descent methods are stable under small perturbations.