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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 317304, 7 pages
http://dx.doi.org/10.1155/2014/317304
Research Article

On Nonsmooth Semi-Infinite Minimax Programming Problem with -Invexity

1Department of Mathematics, Hanshan Normal University, Guangdong 521041, China
2Department of Computer Science, Hanshan Normal University, Guangdong 521041, China
3Science College, Beijing University of Civil Engineering and Architecture, Beijing 102616, China

Received 29 August 2013; Accepted 12 January 2014; Published 4 March 2014

Academic Editor: Josip E. Pečarić

Copyright © 2014 X. L. Liu 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

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz -invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems.