A Projection Hestenes-Stiefel-Like Method for Monotone Nonlinear Equations with Convex Constraints

Abstract

The Hestenes-Stiefel (HS) conjugate gradient (CG) method is generally regarded as one of the most efficient methods for large-scale unconstrained optimization problems. In this paper, we extend a modified Hestenes-Stiefel conjugate gradient method based on the projection technique and present a new projection method for solving nonlinear monotone equations with convex constraints. The search direction obtained satisfies the sufficient descent condition. The method can be applied to solve nonsmooth monotone problems for it is derivative free. Under appropriate assumptions, the method is shown to be globally convergent. Preliminary numerical results show that the proposed method works well and is very efficient.