A family of inertial-relaxed DFPM-based algorithms for solving large-scale monotone nonlinear equations with application to sparse signal restoration

In this paper, combining the inertial-relaxed technique and the Armijo line search technique, we propose a family of inertial-relaxed derivative-free projection methods (DFPMs) for large-scale monotone nonlinear equations. The global convergence of the proposed family is established without the Lipschitz continuity of the underlying mapping. To the best of our knowledge, this is the first convergence result for embedding the inertial-relaxed technique into DFPMs for solving monotone nonlinear equations. Moreover, we propose two inertial-relaxed DFPM-based algorithms with convergence guarantee by embedding two specific search directions into the family. The numerical results on standard monotone nonlinear equations show that our proposed methods are efficient and competitive. Finally, we illustrate the applicability and encouraging efficiency of the proposed methods via applying them to solve sparse signal restoration.