Abstract and Applied Analysis
Volume 2011 (2011), Article ID 432963, 16 pages
http://dx.doi.org/10.1155/2011/432963
Research Article

Second-Order Optimality Conditions for Set-Valued Optimization Problems Under Benson Proper Efficiency

Qilin Wang1 and Guolin Yu2

1College of Sciences, Chongqing Jiaotong University, Chongqing 400074, China
2Research Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan 750021, China

Received 4 October 2011; Accepted 18 November 2011

Academic Editor: D. Anderson

Copyright © 2011 Qilin Wang and Guolin Yu. 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

Some new properties are obtained for generalized second-order contingent (adjacent) epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.