An accelerated double-step derivative-free projection method based algorithm using Picard–Mann iterative process for solving convex constrained nonlinear equations

In this paper, we propose a double-step derivative-free projection method to solve large-scale nonlinear equations with convex constraints, which is an extension of the popular double direction and double-step method for solving unconstrained optimization problems. Its search direction contains the acceleration parameter and the correction parameter obtained by utilizing the approximate Jacobian matrix and the Picard–Mann hybrid iteration process, respectively. We prove the global convergence of the proposed method under the pseudo-monotone property of the mapping. Moreover, the R-linear convergence rate of the proposed method is presented. Numerical experiments verify the effectiveness of the proposed method.