Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 875097, 13 pages
Research Article

A Truncated Descent HS Conjugate Gradient Method and Its Global Convergence

1College of Software, Dongguan University of Technology, Dongguan 523000, China
2College of Mathematics and Physics, Shandong Institute of Light Industry, Jinan 250353, China

Received 2 December 2008; Accepted 8 April 2009

Academic Editor: Ekaterina Pavlovskaia

Copyright © 2009 Wanyou Cheng and Zongguo Zhang. 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.


Recently, Zhang (2006) proposed a three-term modified HS (TTHS) method for unconstrained optimization problems. An attractive property of the TTHS method is that the direction generated by the method is always descent. This property is independent of the line search used. In order to obtain the global convergence of the TTHS method, Zhang proposed a truncated TTHS method. A drawback is that the numerical performance of the truncated TTHS method is not ideal. In this paper, we prove that the TTHS method with standard Armijo line search is globally convergent for uniformly convex problems. Moreover, we propose a new truncated TTHS method. Under suitable conditions, global convergence is obtained for the proposed method. Extensive numerical experiment show that the proposed method is very efficient for the test problems from the CUTE Library.