Characterizations of ɛ-duality gap statements for constrained optimization problems

In this paper we present different regularity conditions that equivalently characterize various ε-duality gap statements (with ε ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ε-subdifferentials. When ε = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.