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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 854125, 7 pages
http://dx.doi.org/10.1155/2013/854125
Research Article

Generalized Minimax Programming with Nondifferentiable ( , )-Invexity

Department of Mathematics, Hanshan Normal University, Guangdong 521041, China

Received 26 November 2012; Accepted 23 December 2012

Academic Editor: C. Conca

Copyright © 2013 D. H. Yuan and X. L. Liu. 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 the generalized minimax programming problem (P) in which functions are locally Lipschitz ( , )-invex. Not only -sufficient but also -necessary optimality conditions are established for problem (P). With -necessary optimality conditions and ( , )-invexity on hand, we construct dual problem (DI) for the primal one (P) and prove duality results between problems (P) and (DI). These results extend several known results to a wider class of programs.