Convergence of the Polak–Ribiére–Polyak conjugate gradient method

In this paper, we consider the global convergence of the Polak–Ribiére–Polyak (abbreviated PRP) conjugate gradient method for unconstrained optimization problems. A new Armijo-type line search is proposed for the original PRP method and some convergence properties are given under some mild conditions. The new Armijo-type line search can make the PRP method choose a suitable initial step size so as to decrease the function evaluations at each iteration and improve the performance of the PRP method. Numerical results show that the PRP method with the new Armijo-type line search is more efficient than other similar methods in practical computation.