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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 131938, 8 pages
http://dx.doi.org/10.1155/2013/131938
Research Article

Optimality Conditions for Nonsmooth Generalized Semi-Infinite Programs

1Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
2Business School, Sichuan University, Chengdu 610064, China

Received 30 July 2013; Accepted 21 August 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 Zhangyou Chen and Zhe Chen. 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

We consider a class of nonsmooth generalized semi-infinite programming problems. We apply results from parametric optimization to the lower level problems of generalized semi-infinite programming problems to get estimates for the value functions of the lower level problems and thus derive necessary optimality conditions for generalized semi-infinite programming problems. We also derive some new estimates for the value functions of the lower level problems in terms of generalized differentiation and further obtain the necessary optimality conditions.