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Journal of Applied Mathematics
Volume 2012, Article ID 946893, 21 pages
http://dx.doi.org/10.1155/2012/946893
Research Article

An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

1Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA
2Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, Arizona 86011-5717, USA

Received 11 October 2011; Revised 10 May 2012; Accepted 24 May 2012

Academic Editor: James Buchanan

Copyright © 2012 John Machacek and Shafiu Jibrin. 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 investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.