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Journal of Applied Mathematics
Volume 2014, Article ID 613205, 9 pages
http://dx.doi.org/10.1155/2014/613205
Research Article

A Novel Approach for Solving Semidefinite Programs

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
2School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
3Department of Basic Science, Henan Mechanical and Electrical Engineering College, Xinxiang 453002, China

Received 2 April 2014; Accepted 3 August 2014; Published 18 August 2014

Academic Editor: Ram N. Mohapatra

Copyright © 2014 Hong-Wei Jiao et al. 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

A novel linearizing alternating direction augmented Lagrangian approach is proposed for effectively solving semidefinite programs (SDP). For every iteration, by fixing the other variables, the proposed approach alternatively optimizes the dual variables and the dual slack variables; then the primal variables, that is, Lagrange multipliers, are updated. In addition, the proposed approach renews all the variables in closed forms without solving any system of linear equations. Global convergence of the proposed approach is proved under mild conditions, and two numerical problems are given to demonstrate the effectiveness of the presented approach.