Higher order weak epiderivatives and applications to duality and optimality conditions

In this paper, the notions of higher order weak contingent epiderivative and higher order weak adjacent epiderivative for a set-valued map are defined. By virtue of higher order weak adjacent (contingent) epiderivatives and Henig efficiency, we introduce a higher order Mond–Weir type dual problem and a higher order Wolfe type dual problem for a constrained set-valued optimization problem (SOP) and discuss the corresponding weak duality, strong duality and converse duality properties. We also establish higher order Kuhn–Tucker type necessary and sufficient optimality conditions for (SOP).