Subdifferentials with degrees of freedom and applications to optimization problems

Abstract

In this work, we first present a new class of generalized differentials, namely subdifferentials with degrees of freedom as well as their applications in nonsmooth optimization problems. We then establish some computation rules for subdifferentials with degree of frecdom of functions under basic qualification constraints. By using these computation rules, we provide necessary and sufficient conditions for unconstraint optmization problems and for optimization problems with geometric constraints.