Two-Step Modulus-Based Synchronous Multisplitting Iteration Methods for Nonlinear Complementarity Problems

Abstract

Two-step modulus-based synchronous multisplitting and symmetric modulus-based synchronous multisplitting accelerated overrelaxation iteration methods are developed for solving large sparse nonlinear complementarity problems. The methods are based on the reformulation of the corresponding problem as a series of equivalent implicit fixed-point equations. This approach includes existing algorithms as special cases and present new models. The convergence of the methods is studied in the case of $H_+$ system matrices. Numerical results confirm the efficiency of the methods proposed.