New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions. (3rd April 2021) - Fang, Donghui; Ansari, Qamrul Hasan; Yao, Jen-Chih
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).