Characterizing the Solution Set for Nonconvex Semi-Infinite Programs Involving Tangential Subdifferentials. (17th February 2021)

• Record Type: Journal Article
• Authors: Long, Xian-Jun; Liu, Juan; Huang, Nan-Jing
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 3(2021)
• Page Start: 279
• Page End: 297
• Publication Date: 2021-02-17
• Subjects: Dini pseudoconvexity -- nonconvex semi-infinite program -- solution set -- tangential subdifferential; 90C26 -- 90C34 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1873366
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The purpose of this paper is to study the characterization of the solution set for nonconvex semi-infinite programming problems related to tangential subdifferentials. We give a necessary optimality condition for the solution set of the nonconvex semi-infinite programming problem. We also prove that the Lagrangian function associated with a fixed Lagrange multiplier is constant on the solution set for semi-infinite programming problems. Finally, by using Dini pseudoconvexity, we obtain two characterizations of the solution set of the problem considered in this paper. Some examples are given to illustrate our results.