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Journal of Applied Mathematics
Volume 2013, Article ID 237428, 7 pages
http://dx.doi.org/10.1155/2013/237428
Research Article

Nonsmooth Multiobjective Fractional Programming with Local Lipschitz Exponential -Invexity

Chung-Jen Junior College of Nursing, Health Sciences and Management, Chia-Yi 62241, Taiwan

Received 3 June 2013; Accepted 4 September 2013

Academic Editor: Gue Lee

Copyright © 2013 Shun-Chin Ho. 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 study nonsmooth multiobjective fractional programming problem containing local Lipschitz exponential -invex functions with respect to and . We introduce a new concept of nonconvex functions, called exponential -invex functions. Base on the generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient solution. Furthermore, employing optimality conditions to perform Mond-Weir type duality model and prove the duality theorems including weak duality, strong duality, and strict converse duality theorem under exponential -invexity assumptions. Consequently, the optimal values of the primal problem and the Mond-Weir type duality problem have no duality gap under the framework of exponential -invexity.