Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 363012, 13 pages
Research Article

ϵ-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

Department of Applied Mathematics, Pukyong National University, Pusan 608-737, South Korea

Received 30 October 2009; Accepted 10 December 2009

Academic Editor: Yeol Je Cho

Copyright © 2010 Gue Myung Lee and Jae Hyoung Lee. 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.


A convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its ϵ-approximate solutions, and then we prove ϵ-weak duality theorem and ϵ-strong duality theorem which hold between the problem and its Wolfe type dual problem. Moreover, we give an example illustrating the duality theorems.