Copyright © 2009 Q. L. Wang and S. J. Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type
dual problem are introduced for a constrained set-valued optimization problem, respectively. Then, corresponding weak duality, strong duality, and converse duality theorems are established.