Conjugation-Based Approach to the ε-Subdifferential of Convex Suprema

Abstract

We provide new characterizations of the ε-subdifferential of the supremum of an arbitrary family of convex functions. The resulting formulas only involve approximate subdifferentials of adequate convex combinations of the data functions. Families of convex functions with a concavity-like property are introduced and their relationship with affine models is studied. The role of the lower semi-continuity of the data functions is also analyzed.