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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 606457, 17 pages
doi:10.1155/2012/606457
Stable Zero Lagrange Duality for DC Conic Programming
College of Mathematics and Statistics, Jishou University, Jishou 416000, China
Received 5 September 2012; Accepted 25 October 2012
Academic Editor: Abdel-Maksoud A. Soliman
Copyright © 2012 D. H. Fang. 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 consider the problems of minimizing a DC function under a cone-convex constraint and a set constraint. By using the infimal convolution of the conjugate functions, we present a new constraint qualification which completely characterizes the Farkas-type lemma and the stable zero Lagrange duality gap property for DC conical programming problems in locally convex spaces.