εε-strict subdifferentials of set-valued maps and optimality conditions

In this paper, first, a new notion of εε-strict subdifferentials of set-valued maps is introduced in a locally convex space. Second, the existence for a εε-strict subdifferential of a set-valued map and an equivalent characterization for εε-strict subgradient of a set-valued map are presented, respectively. Third, a generalized Moreau–Rockafellar theorem with set-valued maps is obtained. Finally, optimality conditions of vector optimization problems with set-valued maps are established in the sense of εε-strict subdifferential.