Weaker conditions for subdifferential calculus of convex functions

Abstract

In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level of generality among those leading to the Hiriart-Urruty and Phelps formula (Hiriart-Urruty and Phelps, 1993 [15]), involving the approximate subdifferential, and the stronger assumption used in the well-known Moreau-Rockafellar formula (Rockafellar 1970, [23]; Moreau 1966, [20]), which only uses the exact subdifferential. We give an application to derive asymptotic optimality conditions for convex optimization.