Global convergence of the DY conjugate gradient method with Armijo line search for unconstrained optimization problems

Abstract

Generally, global convergence of the conjugate gradient methods for unconstrained optimization problems needs Wolfe line search or strong Wolfe line search. In this article, we propose a cautious DY conjugate gradient method and prove that this method with Armijo line search converges globally if the objective function has Lipschitz continuous gradients. We also present some preliminary numerical results to show the efficiency of the proposed method.