A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems

In this paper, a modification to the Polak–Ribiere–Polyak (PRP) nonlinear conjugate gradient method is presented. The proposed method always generates a sufficient descent direction independent of the accuracy of the line search and the convexity of the objective function. Under appropriate conditions, the modified method is proved to possess global convergence under the Wolfe or Armijo-type line search. Moreover, the proposed methodology is adopted in the Hestenes–Stiefel (HS) and Liu–Storey (LS) methods. Extensive preliminary numerical experiments are used to illustrate the efficiency of the proposed method.