An Efficient Algorithm for Min-Max Convex Semi-Infinite Programming Problems. (2nd August 2016)

• Record Type: Journal Article
• Authors: Zhang, Liping; Wu, Soon-Yi
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 8(2016)
• Page Start: 1037
• Page End: 1053
• Publication Date: 2016-08-02
• Subjects: Convex programming -- exchange method -- semi-infinite programming; 90C30 -- 49D39 -- 65K05 -- 65D15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1191033
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: 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.