A Polak–Ribière–Polyak method for solving large-scale nonlinear systems of equations and its global convergence

摘要

A derivative-free conjugate gradient type method for solving large-scale nonlinear systems of equations is presented. In the iterative method, the search direction is based on the Polak–Ribière–Polyak (PRP) conjugate gradient method, and the steplength is determined by a suitable nonmonotone line search. Under appropriate conditions, the global convergence of the proposed method is established. The method is suitable to large-scale problems for the lower storage requirement. It is shown from the numerical results that the method is practically effective.