Accelerated derivative-free method for nonlinear monotone equations with an application

In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three-term derivative-free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133-145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method.