The Ekeland variational principle for set-valued maps involving coderivatives

Abstract

In this paper we use the Fréchet, Clarke, and Mordukhovich coderivatives to obtain variants of the Ekeland variational principle for a set-valued map F and establish optimality conditions for set-valued optimization problems. Our technique is based on scalarization with the help of a marginal function associated with F and estimates of subdifferentials of this function in terms of coderivatives of F.