A derivative-free iterative method for nonlinear monotone equations with convex constraints

Abstract

In this paper, based on the projection strategy, we propose a derivative-free iterative method for large-scale nonlinear monotone equations with convex constraints, which can generate a sufficient descent direction at each iteration. Due to its lower storage and derivative-free information, the proposed method can be used to solve large-scale non-smooth problems. The global convergence of the proposed method is proved under the Lipschitz continuity assumption. Moreover, if the local error bound condition holds, the proposed method is shown to be linearly convergent. Preliminary numerical comparison shows that the proposed method is efficient and promising.