A projection method for convex constrained monotone nonlinear equations with applications

In this paper, we present a projection method to solve monotone nonlinear equations with convex constraints. This method can be viewed as an extension of CG_DESCENT method which is one of the most effective conjugate gradient methods for solving unconstrained optimization problems. Because of derivative-free and low storage, the proposed method can be used to solve large-scale nonsmooth monotone nonlinear equations. Its global convergence is established under some appropriate conditions. Preliminary numerical results show that the proposed method is effective and promising. Moreover, we also successfully use the proposed method to solve the sparse signal reconstruction in compressive sensing.