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Abstract and Applied Analysis
Volume 2014, Article ID 203467, 6 pages
Research Article

A Note on Optimality Conditions for DC Programs Involving Composite Functions

1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2College of Automation, Chongqing University, Chongqing 400030, China
3School of Management, Southwest University of Political Science and Law, Chongqing 401120, China

Received 23 April 2014; Accepted 22 May 2014; Published 29 May 2014

Academic Editor: Chong Li

Copyright © 2014 Xiang-Kai Sun and Hong-Yong Fu. 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.


By using the formula of the ε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator are examined at the end of this paper.