Subdifferential representation formula and subdifferential criteria for the behavior of nonsmooth functions

Abstract

Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be equivalent to certain appropriate conditions in terms of the Clarke subdifferential. The paper provides a systematic study showing that any such condition with the Clarke subdifferential is valid if and only if it holds with any operator representing the Clarke subdifferential like in the subdifferential proximal formula.