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Journal of Applied Mathematics
Volume 2014, Article ID 610612, 8 pages
Research Article

A Novel Self-Adaptive Trust Region Algorithm for Unconstrained Optimization

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

Received 28 August 2013; Revised 18 March 2014; Accepted 19 March 2014; Published 15 April 2014

Academic Editor: Kazutake Komori

Copyright © 2014 Yunlong Lu 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.


A new self-adaptive rule of trust region radius is introduced, which is given by a piecewise function on the ratio between the actual and predicted reductions of the objective function. A self-adaptive trust region method for unconstrained optimization problems is presented. The convergence properties of the method are established under reasonable assumptions. Preliminary numerical results show that the new method is significant and robust for solving unconstrained optimization problems.