A derivative-free projection method for solving convex constrained monotone equations

The CG_DESCENT (CGD) method is one of the most efficient conjugate gradient methods for solving unconstrained optimization problems. However, its applications in some other scenarios are relatively few. In this paper, inspired by one spectral PRP projection method, we extend the CGD method, and establish a derivative-free spectral CGD type projection method to solve large-scale nonlinear monotone equations with convex constraints. Due to it inheriting some nice properties of the conjugate gradient method such as the low memory requirement, the proposed method is very suitable to solve large-scale nonlinear monotone equations. Under appropriate conditions, we prove that the proposed method is globally convergent. Preliminary numerical results show that the proposed method works well.