Duality for composite optimization problem within the framework of abstract convexity. (2nd January 2023)

• Record Type: Journal Article
• Authors: Bednarczuk, Ewa; Tran, The Hung
• Is Part Of: Optimization. Volume 72:Number 1(2023)
• Page Start: 37
• Page End: 80
• Publication Date: 2023-01-02
• Subjects: Abstract convexity -- ε-subdifferentials -- Conjugate dual -- Lagrange dual -- global optimization; 49J27 -- 49J35 -- 49N15 -- 90C46 -- 90C26; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2132822
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. We provide conditions for zero duality gap in conjugate duality. For Lagrange duality, intersection property is applied to obtain zero duality gap. Connection between Lagrange dual and conjugate dual is also established. Examples related to convex and weakly convex functions are given.