Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 258756, 10 pages
doi:10.1155/2009/258756
Research Article

Optimality Conditions and Duality for DC Programming in Locally Convex Spaces

Xianyun Wang

College of Mathematics and Computer Science, Jishou University, Jishou 416000, China

Received 10 February 2009; Revised 25 June 2009; Accepted 25 September 2009

Academic Editor: K. L. Teo

Copyright © 2009 Xianyun Wang. 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

Consider the DC programming problem (PA) inf⁡x∈X{f(x)−g(Ax)}, where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, respectively, and A is a linear operator from X to Y. By using the properties of the epigraph of the conjugate functions, the optimality conditions and strong duality of (PA) are obtained.