Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 435495, 8 pages
http://dx.doi.org/10.5402/2012/435495
Research Article

A Descent Dai-Liao Conjugate Gradient Method Based on a Modified Secant Equation and Its Global Convergence

Department of Mathematics, University of Patras, 265-00 Patras, Greece

Received 31 August 2011; Accepted 20 October 2011

Academic Editors: K. Eom and R. Joan-Arinyo

Copyright © 2012 Ioannis E. Livieris and Panagiotis Pintelas. 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 conjugate gradient method which is based on the study of the Dai-Liao conjugate gradient method. An important property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. Moreover, it achieves a high-order accuracy in approximating the second-order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. (2010). Under mild conditions, we establish that the proposed method is globally convergent for general functions provided that the line search satisfies the Wolfe conditions. Numerical experiments are also presented.