A Nonlinear Hybridization of Polak-Ribiere-Polyak and Fletcher- Revees Conjugate Gradient Methods

Using a quadratic relaxation of a hybrid conjugate gradient parameter proposed by Gilbert and Nocedal, two hybridizations of the Polak-Ribiere-Polyak and Fletcher-Revees conjugate gradient methods is suggested. In the proposed methods, the hybridization parameter is obtained based on a conjugacy condition. Under proper conditions, it can be shown that the suggested methods are globally convergent. Numerical comparisons demonstrating the efficiency of one of the newly proposed methods are reported.