An inertial-double-projection-based algorithm for large-scale nonlinear systems of monotone equations

In this paper, we propose a derivative-free algorithm for solving large-scale nonlinear systems of monotone equations. This algorithm incorporates a pivotal step inspired by double projection methods, which is further refined through an inertial approach to approximate the solution more effectively. The global convergence of the new algorithm is investigated under some mild conditions. The results of some numerical tests, along with their performance profiles, demonstrate the algorithm's efficacy.