Supermemory gradient methods for monotone nonlinear equations with convex constraints

This paper presents two new supermemory gradient algorithms for solving convex-constrained nonlinear monotone equations, which combine the idea of supermemory gradient method with the projection method. The feature of these proposed methods is that at each iteration, they do not require the Jacobian information and solve any subproblem, even if they do not store any matrix. Thus, they are suitable for solving large-scale equations. Under mild conditions, the proposed methods are shown to be globally convergent. Preliminary numerical results show that the proposed methods are efficient and can be applied to solve large-scale nonsmooth equations.