Journal of Applied Mathematics
Volume 2012 (2012), Article ID 617485, 7 pages
Research Article

Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Chongqing Key Laboratory of Operations Research and System Engineering, Chongqing Normal University, Chongqing 400047, China

Received 6 May 2012; Revised 1 August 2012; Accepted 15 August 2012

Academic Editor: Huijun Gao

Copyright © 2012 Zhe Chen. 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.


We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature.