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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 527183, 5 pages
http://dx.doi.org/10.1155/2013/527183
Research Article

New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

1Department of General Education, National Army Academy, Taoyuan 320, Taiwan
2Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan

Received 29 July 2012; Accepted 1 January 2013

Academic Editor: Jen Chih Yao

Copyright © 2013 Yi-Chou Chen and Wei-Shih Du. 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 a nondifferentiable fractional programming problem as follows: subject to , where is a semiconnected subset in a locally convex topological vector space , , and , . If , , and , , are arc-directionally differentiable, semipreinvex maps with respect to a continuous map satisfying and , then the necessary and sufficient conditions for optimality of are established.