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.