A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence

In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method. An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective function. This property is independent of the line search used. Moreover, if exact line search is used, the method reduces to the ordinary PRP method. Under appropriate conditions, we show that the modified PRP method with Armijo-type line search is globally convergent. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.