A subspace minimization conjugate gradient method for nonlinear monotone equations with convex constraints

The subspace minimization conjugate gradient method is currently one of the popular optimization methods. Based on this method and the projection technique, in this paper we propose a three-term subspace minimization conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. The search direction is obtained by minimizing the quadratic approximate function in a three-dimensional subspace, and satisfies the sufficient descent condition. The global convergence of the proposed algorithm is proved under some appropriate conditions. Numerical results indicate the effectiveness of the proposed algorithm.