A Modified LS Conjugate Gradient Method and Its Global Convergence

In this paper, we propose a modified Liu-Storey conjugate gradient method for solving unconstrained optimization problem. The presented method possesses the sufficient descent property independent of the line search used. Under the suitable conditions, we show that the modified LS method with Armijo-type line search is globally convergent. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.