Journal of Applied Mathematics
Volume 2012 (2012), Article ID 692325, 9 pages
http://dx.doi.org/10.1155/2012/692325
Research Article

Sufficient Optimality and Sensitivity Analysis of a Parameterized Min-Max Programming

Huijuan Xiong,1 Yu Xiao,2 and Chaohong Song1

1College of Science, Huazhong Agricultural University, Wuhan 430070, China
2School of Basic Science, East China Jiaotong University, Nanchang 330000, China

Received 4 June 2012; Accepted 17 July 2012

Academic Editor: Jian-Wen Peng

Copyright © 2012 Huijuan Xiong et al. 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

Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient optimality of the parameterized min-max programming is discussed first. Moreover, under a convex assumption on the objective function, a subdifferential computation formula of the marginal function is obtained. The assumptions are satisfied naturally for some application problems. Moreover, the formulae based on these assumptions are concise and convenient for algorithmic purpose to solve the applications.