Advances in Operations Research
Volume 2009 (2009), Article ID 909753, 22 pages
doi:10.1155/2009/909753
Research Article

A Trust-Region-Based BFGS Method with Line Search Technique for Symmetric Nonlinear Equations

Gonglin Yuan,1 Shide Meng,2 and Zengxin Wei1

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics and Computer Science, Yulin Teacher's College, Yulin, Guangxi 537000, China

Received 29 April 2009; Revised 19 August 2009; Accepted 28 October 2009

Academic Editor: Khosrow Moshirvaziri

Copyright © 2009 Gonglin Yuan 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 trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given method is competitive to the normal trust region method.