Higher Order Mond-Weir Duality for Super Efficient Solutions of Set-Valued Optimization

Abstract

In real normed linear spaces,by virtue of the cone-directed higher order generalized adjacent derivatives,a higher order Mond-Weir dual problem for a constrained set-valued optimization is considered in the sense of super efficient solutions.Under the assumption of generalized cone-convexity,with the help of the properties of cone-directed higher order generalized adjacent derivatives by applying separate theorem for convex sets,a strong duality theorem is established.By taking advantage of the scalarization theorem for a super efficient point,a converse duality theorem is obtained.