Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions

Abstract EN

The notions of higher-order weakly generalized contingent epiderivative and higher-order weakly generalized adjacent epiderivative for set-valued maps are proposed.

By virtue of the higher-order weakly generalized contingent (adjacent) epiderivatives, both necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map.

The imposed assumptions are relaxed in comparison with those of recent results in the literature.

Examples are provided to show some advantages of our notions and results.