Set-valued optimization in variable preference structures with new variants of generalized convexity. (2nd January 2023)

• Record Type: Journal Article
• Authors: Diem, Huynh Thi Hong
• Is Part Of: Optimization. Volume 72:Number 1(2023)
• Page Start: 163
• Page End: 188
• Publication Date: 2023-01-02
• Subjects: local and global extrema relations -- optimality conditions -- duality -- variants of generalized convexity -- Gateaux variation; 90C46 -- 49J53 -- 90C30 -- 90C26 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2158035
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: A set-valued optimization problem with variable preferences is considered. Relations between local and global solutions, optimality conditions, and Wolfe and Mond-Weir duality properties are studied. Both minimal and nondominated solutions are discussed with general variable preferences. The results are proved for three main types of solutions in vector optimization: weak, Pareto, and strong solutions. New variants of generalized derivatives and convexity are proposed and used in all the results.