Convergence of Nonlinear Conjugate Gradient Methods

Abstract

This paper proves that a simplified Armijo-type line search can ensure the global convergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for unconstrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.