Regularity Conditions for Strong Duality in Evenly Convex Optimization Problems. An Application to Fenchel Duality

Abstract

Via perturbational approach, we give an alternative dual problem for a general infinite dimensional optimization primal one, by means of a conjugation scheme based on generalized convex conjugation theory, rather than the classical Fenchel conjugation. Two sufficient regularity conditions for strong duality are stated, where the evenly convexity of the perturbation function plays a fundamental role. One of these conditions has been obtained due to the relationship between evenly convexity and cs-closedness, allowing us also to derive new properties for evenly convex sets and functions. The regularity conditions in the general setting are applied to the Fenchel primal-dual problem, and a comparison between them and an already existing closedness-type regularity condition for Fenchel duality is studied.