E-SUPER EFFICIENCY OF SET-VALUED OPTIMIZATION PROBLEMS INVOLVING IMPROVEMENT SETS

In this paper, E-super efficiency of set-valued optimization problems is investigated. Firstly, based on the improvement set, a new notion of E-super efficient point is introduced in real locally convex spaces. Secondly, under the assumption of near E-subconvexlikeness of set-valued maps, scalarization theorems of set-valued optimization problems are established in the sense of E-super efficiency. Finally, Lagrange multiplier theorems of set-valued optimization problems are obtained in the sense of E-super efficiency.