Globally convergence of nonlinear conjugate gradient method for unconstrained optimization

Abstract

The conjugate gradient method is a useful and powerful approach for solving large-scale minimization problems. In this paper, a new nonlinear conjugate gradient method is proposed for large-scale unconstrained optimization. This method include the already existing two practical nonlinear conjugate gradient methods, to combine the nice global convergence properties of Fletcher-Reeves method (abbreviated FR) and the good numerical performances of the Polak–Ribiere–Polyak method (abbreviated PRP), which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. Our numerical results show that of the new method is very efficient for the given test problems. In addition we will study the methods related to the new nonlinear conjugate gradient method.