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.