New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions
Donghui Fang, Qamrul Hasan Ansari, Jen‐Chih Yao · Optimization · 2020
We consider the following DC composite optimization problem (P): infx∈Xf1(x)−f2(x)+g1(h(x))−g2(h(x)), where f1,f2 and g1,g2 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).