Optimality of approximate solutions in set-valued optimization involving subarcwise connected cone-convexity

Abstract:

This note deals with the optimality conditions of approximate solutions in set-valued optimization problems involving generalized arcwise connected convexity in terms of the contingent epiderivative. Firstly, the concept of subarcwise connected cone-convex set-valued mapping is introduced. Then, the two roperties of subarcwise connected cone-convex set-valued mapping are derived. Finally, the sufficient optimality conditions are established for weak approximate efficient and strong approximate efficient elements respectively under the assumption of subarcwise connected cone-convexity.