Higher-order Optimality Conditions and Duality for Approximate Solutions in Non-convex Set-valued Optimization

Abstract

This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps. Firstly, under the assumption of near cone-subconvexlikeness for set-valued maps, the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem. Then, applications to Mond-Weir type dual problem are presented.