Conjugate Duality for Constrained Vector Optimization in Abstract Convex Frame. (18th August 2019)

• Record Type: Journal Article
• Authors: Yao, Chaoli; Li, Shengjie
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 11(2019)
• Page Start: 1242
• Page End: 1267
• Publication Date: 2019-08-18
• Subjects: Constrained vector optimization -- conjugate duality -- abstract convexity -- set-valued topical function -- image space analysis; 90C29 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1599910
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This article focuses on a conjugate duality for a constrained vector optimization in the framework of abstract convexity. With the aid of the extension for the notion of infimum to the vector space, a set-valued topical function and the corresponding conjugate map, subdifferentials are presented. Following this, a conjugate dual problem is proposed via this conjugate map. Then, inspired by some ideas in the image space analysis, some equivalent characterizations of the zero duality gap are established by virtue of the subdifferentials.