Global convergence of the Polak-Ribière-Polyak conjugate gradient method with an Armijo-type inexact line search for nonconvex unconstrained optimization problems

摘要

We propose two algorithms for nonconvox unconstrained optimization problems that employ Polak-Ribicro-Polyak conjugate gradient formula and new inexact line search techniques. We show that the new algorithms converge globally if the function to be minimized has Lipschitz continuous gradients. Preliminary numerical results show that the proposed methods for particularly chosen line search conditions are very promising.