Journal of Applied Mathematics

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

John Machacek and Shafiu Jibrin

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 946893, 21 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495286

Digital Object Identifier
doi:10.1155/2012/946893

Mathematical Reviews number (MathSciNet)
MR2970422

Zentralblatt MATH identifier
1254.90155

Citation

Machacek, John; Jibrin, Shafiu. An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers. J. Appl. Math. 2012 (2012), Article ID 946893, 21 pages. doi:10.1155/2012/946893. https://projecteuclid.org/euclid.jam/1355495286


Export citation