Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations

Abstract

In this paper, we present a modification of Polak–Ribie´re–Polyak (PRP) conjugate gradient method for solving system of monotone nonlinear equations which is a combination of spectral conjugate gradient method and the hyperplane projection technique. The method is based on two methods for unconstrained optimization proposed by Wan et al. (2011) and Sun (2015). We obtained a new search direction by the use of a different formula for the conjugate gradient parameter. The search direction satisfies the sufficient descent condition and the global convergence of the method is established under some assumptions. Preliminary numerical comparison with some existing methods shows the efficiency of the proposed method.