A descent Dai-Liao conjugate gradient method based on a modified secant equation and its global convergence (Q408488)

Summary: 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 \textit{S. Babaie-Kafaki, R. Ghanbari} and \textit{N. Mahdavi-Amiri} [J. Comput. Appl. Math. 234, No. 5, 1374--386 (2010; Zbl 1202.65071)]. 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.