Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 462637, 18 pages
doi:10.1155/2009/462637
Research Article

Higher-Order Weakly Generalized Adjacent Epiderivatives and Applications to Duality of Set-Valued Optimization

Q. L. Wang1,2 and S. J. Li1

1College of Mathematics and Science, Chongqing University, Chongqing 400044, China
2College of Sciences, Chongqing Jiaotong University, Chongqing 400074, China

Received 6 February 2009; Accepted 8 July 2009

Academic Editor: Kok Teo

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.

Abstract

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.