Higher-order weakly generalized epiderivatives and applications to optimality conditions

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. © 2012 qilin wang and guolin yu.