Global convergence of the original Liu-Storey conjugate gradient method

Abstract

The original Liu-Storey (LS) method is one of the most effective nonlinear conjugate gradient methods for solving unconstrained optimization problems.Its global convergence is only obtained by using some descent backtracking line searches, which can force the original LS method to generate the sufficient descent direction at each iteration.In this paper, we prove the global convergence of the original LS method with a non-declining backtracking line search.