$$\varepsilon $$ ε -Subdifferential as an Enlargement of the Subdifferential

Abstract

This work introduces a remarkable property of enlargements of maximal monotone operators. The basic tool in our analysis is a family of enlargements, introduced by Svaiter. Using the fact that the $$\varepsilon $$ -subdifferential operator can be regarded as an enlargement of the subdifferential, a sufficient condition for some calculus rules in convex analysis can be provided. We give several corollaries about $$\varepsilon $$ -subdifferential and extend one of them to arbitrary enlargement.