Lagrange duality for evenly convex optimization problems (Q255070)

A subset of a locally convex space is called evenly convex iff it is the intersection of an arbitrary family (possibly empty) of open halfspaces. This class of sets was introduced in the finite-dimensional case by Fenchel in order to extend the polarity theory to non-closed and convex sets. An evenly convex function on a locally convex space is an extended real-valued function, whose epigraph is an evenly convex set. In this paper, the authors consider an infinite-dimensional optimization problem, for which both objective function and constraints are evenly convex. They recover the classical Lagrange dual problem for it, via perturbational approach. The aim of the paper is to establish regularity conditions for strong duality between both problems, formulated in terms of even convexity.