A dual parameterization approach to linear-quadratic semi-infinite programming problems

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805725

Y. Liu, K. Teo, S. Ito

引用次数: 13

Abstract

Semi-infinite programming problems are special optimization problems in which a cost is to be minimized subject to infinitely many constraints. This class of problems has many real-world applications. In this paper, we consider a class of linear-quadratic semi-infinite programming problems. Using the duality theory, the dual problem is obtained, where the decision variables are measures. A new parameterization scheme is developed for approximating these measures. On this bases, an efficient algorithm for computing the solution of the dual problem is obtained. Rigorous convergence results are given to support the algorithm. The solution of the primal problem is easily obtained from that of the dual problem. For illustration, three numerical examples are included.

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线性二次半无限规划问题的对偶参数化方法

半无限规划问题是一种特殊的优化问题，其目标是在无限多个约束条件下使成本最小化。这类问题有许多实际应用。本文研究了一类线性二次半无限规划问题。利用对偶理论，得到了决策变量为测度的对偶问题。提出了一种新的参数化方案来逼近这些度量。在此基础上，给出了一种计算对偶问题解的有效算法。给出了严格的收敛结果来支持该算法。原始问题的解很容易由对偶问题的解得到。为了说明，本文给出了三个数值例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.