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Journal of Optimization
Volume 2014, Article ID 237279, 8 pages
http://dx.doi.org/10.1155/2014/237279
Research Article

A Nonmonotone Adaptive Trust Region Method Based on Conic Model for Unconstrained Optimization

Department of Mathematics and Physics, Shandong Jiaotong University, Ji’nan, Shandong Province 250023, China

Received 20 August 2013; Accepted 29 November 2013; Published 27 January 2014

Academic Editor: Adil M. Bagirov

Copyright © 2014 Zhaocheng Cui. 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 propose a nonmonotone adaptive trust region method for unconstrained optimization problems which combines a conic model and a new update rule for adjusting the trust region radius. Unlike the traditional adaptive trust region methods, the subproblem of the new method is the conic minimization subproblem. Moreover, at each iteration, we use the last and the current iterative information to define a suitable initial trust region radius. The global and superlinear convergence properties of the proposed method are established under reasonable conditions. Numerical results show that the new method is efficient and attractive for unconstrained optimization problems.