Optimality and duality in set-valued optimization utilizing limit sets

Abstract

This paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

Keywords

• limit set
• optimality conditions
• set-valued optimization
• nearly cone-subconvexlike
• duality
• 90c29
• 90c46
• 26b25