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International Journal of Mathematics and Mathematical Sciences
Volume 2013, Article ID 284046, 10 pages
Research Article

Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized -Univex Functions

1Department of Mathematics and Science, National Taiwan Normal University, Linkou Campus, Renai Road, Section 1, Linkou Shiang, Taipei 24499, Taiwan
2Department of Mathematics, National Central University, Zhongli, Taoyuan, Taiwan

Received 11 July 2013; Accepted 23 October 2013

Academic Editor: Onesimo Hernandez Lerma

Copyright © 2013 Jen-Chwan Liu and Chun-Yu 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.


We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized -univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized -univex functions.