The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Stefan M Stefanov - One of the best experts on this subject based on the ideXlab platform.
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minimization of a strictly convex separable function subject to convex separable Inequality Constraint and box Constraints
Journal of Interdisciplinary Mathematics, 2009Co-Authors: Stefan M StefanovAbstract:Abstract A minimization problem with strictly convex separable objective function subject to a convex separable Inequality Constraint of the form “less than or equal to” and bounds on the variables is considered. Necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. An iterative algorithm of polynomial complexity for solving such problems is suggested and its convergence is proved. Modifications of this algorithm are proposed in connection with some extensions of the considered problem as well as in order to avoid some computational difficulties. Examples of important convex functions for the problem under consideration and computational results are presented.
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an efficient method for minimizing a convex separable logarithmic function subject to a convex Inequality Constraint or linear equality Constraint
Journal of Applied Mathematics and Decision Sciences, 2006Co-Authors: Stefan M StefanovAbstract: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.
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minimization of a convex linear fractional separable function subject to a convex Inequality Constraint or linear Inequality Constraint and bounds on the variables
Applied Mathematics Research Express, 2006Co-Authors: Stefan M StefanovAbstract:We consider the problem of minimizing a convex linear-fractional separable function over a feasible region defined by a convex Inequality Constraint or linear Inequality Constraint, and bounds on the variables (box Constraints). These problems are interesting from both theoretical and practical points of view because they arise in some mathematical programming problems and in various practical problems. Polynomial algorithms for solving such problems are proposed and their convergence is proved. Some examples and results of numerical experiments are also presented.
Nikolaus Hansen - One of the best experts on this subject based on the ideXlab platform.
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augmented lagrangian Constraint handling for cma es case of a single linear Constraint
Parallel Problem Solving from Nature, 2016Co-Authors: Asma Atamna, Anne Auger, Nikolaus HansenAbstract:We consider the problem of minimizing a function f subject to a single Inequality Constraint \(g(\mathbf x ) \le 0\), in a black-box scenario. We present a covariance matrix adaptation evolution strategy using an adaptive augmented Lagrangian method to handle the Constraint. We show that our algorithm is an instance of a general framework that allows to build an adaptive Constraint handling algorithm from a general randomized adaptive algorithm for unconstrained optimization. We assess the performance of our algorithm on a set of linearly constrained functions, including convex quadratic and ill-conditioned functions, and observe linear convergence to the optimum.
Rujun Jiang - One of the best experts on this subject based on the ideXlab platform.
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socp reformulation for the generalized trust region subproblem via a canonical form of two symmetric matrices
Mathematical Programming, 2018Co-Authors: Rujun JiangAbstract:We investigate in this paper the generalized trust region subproblem (GTRS) of minimizing a general quadratic objective function subject to a general quadratic Inequality Constraint. By applying a simultaneous block diagonalization approach, we obtain a congruent canonical form for the symmetric matrices in both the objective and Constraint functions. By exploiting the block separability of the canonical form, we show that all GTRSs with an optimal value bounded from below are second order cone programming (SOCP) representable. Our result generalizes the recent work of Ben-Tal and den Hertog (Math. Program. 143(1–2):1–29, 2014), which establishes the SOCP representability of the GTRS under the assumption of the simultaneous diagonalizability of the two matrices in the objective and Constraint functions. We then derive a closed-form solution for the GTRS when the two matrices are not simultaneously diagonalizable. We further extend our method to two variants of the GTRS in which the Inequality Constraint is replaced by either an equality Constraint or an interval Constraint.
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socp reformulation for the generalized trust region subproblem via a canonical form of two symmetric matrices
arXiv: Optimization and Control, 2016Co-Authors: Rujun JiangAbstract:We investigate in this paper the generalized trust region subproblem (GTRS) of minimizing a general quadratic objective function subject to a general quadratic Inequality Constraint. By applying a simultaneous block diagonalization approach, we obtain a congruent canonical form for the symmetric matrices in both the objective and Constraint functions. By exploiting the block separability of the canonical form, we show that all GTRSs with an optimal value bounded from below are second order cone programming (SOCP) representable. Our result generalizes the recent work of Ben-Tal and Hertog (Math. Program. 143(1-2):1-29, 2014), which establishes the SOCP representability of the GTRS under the assumption of the simultaneous diagonalizability of the two matrices in the objective and Constraint functions. Compared with the state-of-the-art approach to reformulate the GTRS as a semi-definite programming problem, our SOCP reformulation delivers a much faster solution algorithm. We further extend our method to two variants of the GTRS in which the Inequality Constraint is replaced by either an equality Constraint or an interval Constraint. Our methods also enable us to obtain simplified versions of the classical S-lemma, the S-lemma with equality, and the S-lemma with interval bounds.
Weihai Zhang - One of the best experts on this subject based on the ideXlab platform.
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study on indefinite stochastic linear quadratic optimal control with Inequality Constraint
Journal of Applied Mathematics, 2013Co-Authors: Weihai ZhangAbstract:This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an Inequality Constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid Constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.
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Discrete-time indefinite stochastic linear quadratic optimal control: Inequality Constraint case
2013Co-Authors: Weihai ZhangAbstract:It is known that the Karush-Kuhn-Tucker (KKT) theorem gives necessary conditions for the existence of optimal solutions to constrained optimization problems. It is shown that a class of discrete-time indefinite stochastic linear quadratic (LQ) optimal control problems with an Inequality Constraint on terminal state, can be transformed into a mathematical programming problem with equality and Inequality constrains. In this paper, the KKT condition for the existence of optimal linear state feedback controllers is given. More importantly, the previous results on discrete-time stochastic LQ optimal control without Constraints or with equality Constraints, can be viewed as corollaries of the main theorems of this paper.
Yiguang Hong - One of the best experts on this subject based on the ideXlab platform.
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generalized nash equilibrium seeking strategy for distributed nonsmooth multi cluster game
Automatica, 2019Co-Authors: Xianlin Zeng, Jie Chen, Shu Liang, Yiguang HongAbstract:This paper investigates the distributed strategy design to find generalized Nash equilibria (GNE) of multi-cluster games with nonsmooth payoff functions, a coupled nonlinear Inequality Constraint, and set Constraints. In this game, each cluster is composed of a group of agents and is a virtual noncooperative player, who minimizes its payoff function; each agent only uses its local payoff function, local feasible set and partial information of the coupled Inequality Constraint, and communicates with its neighbors. To solve the GNE problem, we propose a distributed nonsmooth algorithm using a projected differential inclusion and establish the convergence analysis of the proposed algorithm. A numerical application is given for illustration.
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on convergence rate of distributed stochastic gradient algorithm for convex optimization with Inequality Constraints
Siam Journal on Control and Optimization, 2016Co-Authors: Deming Yuan, Yiguang HongAbstract:In this paper, we consider an optimization problem, where multiple agents cooperate to minimize the sum of their local individual objective functions subject to a global Inequality Constraint. We propose a class of distributed stochastic gradient algorithms that solve the problem using only local computation and communication. The implementation of the algorithms removes the need for performing the intermediate projections. For strongly convex optimization, we employ a smoothed Constraint incorporation technique to show that the algorithm converges at an expected rate of $\mathcal{O}(\ln T / T)$ (where $T$ is the number of iterations) with bounded gradients. For non-strongly convex optimization, we use a reduction technique to establish an $\mathcal{O}(1/\sqrt{T})$ convergence rate in expectation. Finally, a numerical example is provided to show the convergence of the proposed algorithms.