Minimax Theorem for Two Set-Valued Mappings with Nonconvex Domains. (23rd August 2021)

• Record Type: Journal Article
• Authors: Zhang, Qing-bang
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 12(2021)
• Page Start: 1444
• Page End: 1460
• Publication Date: 2021-08-23
• Subjects: Hausdorff topological vector spaces -- minimax theorem -- S-convcavelike -- S-convexlike; 49J53 -- 49K35; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1965162
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we obtain the operational properties of the set MaxA ( MaxW A, MinA and MinW A ) of a set A in the sense of vector optimization and its' applications to the judgment of the convexity and concavity of a set-valued mapping. By using the separation theorem of convex sets, some minimax theorems of two set-valued mappings have proved in the nonconvex sets. Simultaneously, two examples are given to show our results.