On Fenchel c-conjugate dual problems for DC optimization: characterizing weak, strong and stable strong duality

TL;DR

This paper develops Fenchel-type dual problems for DC optimization using c-conjugation, providing characterizations of various duality conditions and conditions linking their existence.

Contribution

It introduces dual problems based on c-conjugation for DC optimization and characterizes different duality types and their interrelations.

Findings

Characterization of weak, strong, and stable strong duality conditions.

Conditions linking the existence of strong and stable strong duality.

Application of c-conjugation to duality analysis in DC optimization.

Abstract

In this paper we present two Fenchel-type dual problems for a DC (difference of convex functions) optimization primal one. They have been built by means of the c-conjugation scheme, a pattern of conjugation which has been shown to be suitable for evenly convex functions. We study characterizations of weak, strong and stable strong duality for both pairs of primal-dual problems. We also give conditions which relate the existence of strong and stable strong duality for both pairs.