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Journal of Mathematics
Volume 2015, Article ID 456392, 9 pages
http://dx.doi.org/10.1155/2015/456392
Research Article

Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method

Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86011-5717, USA

Received 31 August 2015; Accepted 30 September 2015

Academic Editor: Baoding Liu

Copyright © 2015 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 study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem by using Infeasible Newton’s method applied to the KKT system of equations which can be started from any point. We implement the method using backtracking line search technique and also study the effect of large weights on the method. We use numerical experiments to compare Infeasible Newton’s method with Standard Newton’s method. The results show that Infeasible Newton’s method moves in the interior of the feasible regions often very quickly, starting from any point. We recommend it as a method for finding an interior point by setting each weight to be 1. It appears to work better than Standard Newton’s method in finding the weighted analytic center when none of weights is very large relative to the other weights. However, we find that Infeasible Newton’s method is more sensitive than Standard Newton’s method to large variation in the weights.