An Efficient Subspace Minimization Conjugate Gradient Method for Solving Nonlinear Monotone Equations with Convex Constraints

The subspace minimization conjugate gradient (SMCG) methods proposed by Yuan and Store are efficient iterative methods for unconstrained optimization, where the search directions are generated by minimizing the quadratic approximate models of the objective function at the current iterative point. Although the SMCG methods have illustrated excellent numerical performance, they are only used to solve unconstrained optimization problems at present. In this paper, we extend the SMCG methods and present an efficient SMCG method for solving nonlinear monotone equations with convex constraints by combining it with the projection technique, where the search direction is sufficiently descent.Under mild conditions, we establish the global convergence and R-linear convergence rate of the proposed method. The numerical experiment indicates that the proposed method is very promising.