New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions. (3rd April 2021)

• Record Type: Journal Article
• Authors: Fang, Donghui; Ansari, Qamrul Hasan; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 777
• Page End: 803
• Publication Date: 2021-04-03
• Subjects: Regularity condition -- strong duality -- zero duality gap property -- composite optimization problem -- DC programming; 90C26 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1737864
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We consider the following DC composite optimization problem (P): inf x ∈ X f 1 ( x ) − f 2 ( x ) + g 1 ( h ( x ) ) − g 2 ( h ( x ) ), where f 1, f 2 and g 1, g 2 are proper convex functionals defined on locally convex Hausdorff topological vector spaces X and Y respectively, and h is a proper K -convex mapping from X to Y . By using the properties of the epigraph of the conjugate functions, we introduce some new regularity conditions and obtain complete characterizations for weak / strong / stable Fenchel dualities and for zero / stable zero duality gap properties of problem (P).