Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 819607, 13 pages
http://dx.doi.org/10.1155/2012/819607
Research Article

A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming

Aiqun Huang1,2 and Chengxian Xu1

1School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi, Xi'an 710049, China
2School of Mathematics and Statistics, Huazhong University of Science and Technology, Hubei, Wuhan 430074, China

Received 17 May 2012; Accepted 29 June 2012

Academic Editor: Soohee Han

Copyright © 2012 Aiqun Huang and Chengxian Xu. 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

When using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, based on a semismooth equation reformulation using Fischer's function, we propose a filter method with trust region for solving large-scale SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.