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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 986317, 6 pages
http://dx.doi.org/10.1155/2013/986317
Research Article

A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

College of Mathematics, Honghe University, Mengzi 661199, China

Received 16 December 2012; Accepted 20 March 2013

Academic Editor: Theodore E. Simos

Copyright © 2013 Can Li. 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 are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.