A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

Abstract

In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and converse duality theorems, respectively.

Keywords

• set-valued optimization problems
• higher-order weak adjacent epiderivatives
• higher-order mond-weir type dual
• benson proper efficiency