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

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.