An Efficient Algorithm for Min-Max Convex Semi-Infinite Programming Problems

In this article, we consider the convex min-max problem with infinite constraints. We propose an exchange method to solve the problem by using efficient inactive constraint dropping rules. There is no need to solve the maximization problem over the metric space, as the algorithm has merely to find s...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2016-08, Vol.37 (8), p.1037-1053
Main Authors: Zhang, Liping, Wu, Soon-Yi
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convex programming
Exchange
exchange method
Iterative methods
Mathematical analysis
Mathematical models
Maximization
Metric space
semi-infinite programming
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Summary:In this article, we consider the convex min-max problem with infinite constraints. We propose an exchange method to solve the problem by using efficient inactive constraint dropping rules. There is no need to solve the maximization problem over the metric space, as the algorithm has merely to find some points in the metric space such that a certain criterion is satisfied at each iteration. Under some mild assumptions, the proposed algorithm is shown to terminate in a finite number of iterations and to provide an approximate solution to the original problem. Preliminary numerical results with the algorithm are promising. To our knowledge, this article is the first one conceived to apply explicit exchange methods for solving nonlinear semi-infinite convex min-max problems.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2016.1191033