A PRP-based residual method for large-scale monotone nonlinear equations

摘要

This paper presents a derivative-free residual method for solving large-scale monotone nonlinear equations which may be nonsmooth. The method is constructed by replacing the gradients of the unmodified Polak–Ribière–Polyak (PRP) nonlinear conjugate gradient method with the residuals and combining the hyperplane projection technique. Under suitable conditions, we show that the proposed method converges globally in the sense that the whole iterative sequence converges to a solution of the problem. Some numerical results are reported to show its efficiency.