Spectral Algorithms with Inertial-strategy for Constrained System of Nonlinear Equations

Abstract

In this work, we proposed two modified spectral algorithms for solving a system of nonlinear monotone equations with convex constraints. We have introduced an inertial step in these algorithms to investigate its effect on the iteration process. We have shown that the two proposed algorithms are sufficiently descent and bounded, and consequently, we have established the global convergence under some suitable suppositions. We conducted some numerical experiments and compared the results with four existing methods, one of which, is an inertial-based method, and the other three with no inertia. Our numerical experiments indicated that incorporating the inertial step in a nonlinear system of equations algorithms has a significant advantage in accelerating the iteration process. Interestingly, we have applied one of the two proposed algorithms in motion control involving a 2D joint planar robotic manipulator.