Global Convergence Properties of Conjugate Gradient Methods for Optimization

Abstract

This paper explores the convergence of nonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes of methods that are globally convergent on smooth, nonconvex functions. Some properties of the Fletcher–Reeves method play an important role in the first family, whereas the second family shares an important property with the Polak–Ribière method. Numerical experiments are presented.