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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 478407, 6 pages
http://dx.doi.org/10.1155/2013/478407
Research Article

A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization

School of Mathematics and Statistics, Beihua University, Jilin 132013, China

Received 8 June 2013; Accepted 4 September 2013

Academic Editor: Bo-Qing Dong

Copyright © 2013 Yang Weiwei 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

We present a new Newton-like method for large-scale unconstrained nonconvex minimization. And a new straightforward limited memory quasi-Newton updating based on the modified quasi-Newton equation is deduced to construct the trust region subproblem, in which the information of both the function value and gradient is used to construct approximate Hessian. The global convergence of the algorithm is proved. Numerical results indicate that the proposed method is competitive and efficient on some classical large-scale nonconvex test problems.