I.E. Livieris and P. Pintelas. A descent Dai-Liao conjugate gradient method based on a modified secant equation and its global convergence. ISRN Computational Mathematics, 2012.
Abstract: In this paper, 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. (J. Comput. Appl. Math. 234:1374-1386, 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.