A hybridization of the Polak-Ribière-Polyak and Fletcher-Reeves conjugate gradient methods

Abstract

In order to achieve a theoretically effective and numerically efficient method for solving large-scale unconstrained optimization problems, a hybridization of the Fletcher-Reeves and Polak-Ribiere-Polyak conjugate gradient methods is proposed. In the method, the hybridization parameter is computed such that the generated search directions approach to the search directions of the efficient three-term conjugate gradient method proposed by Zhang et al., to the extent possible. Under proper conditions, global convergence of the method is established without convexity assumption on the objective function. The method is numerically compared with the three-term conjugate gradient method proposed by Zhang et al. and a modified version of the Polak-Ribiere-Polyak method suggested by Gilbert and Nocedal. Comparative testing results demonstrating the efficiency of the proposed method are reported.