An Efficient Class of Modulus-Based Matrix Splitting Methods for Nonlinear Complementarity Problems

In this paper, we present an efficient method for finding a numerical solution for nonlinear complementarity problems (NCPs). We first reformulate an NCP as an equivalent system of fixed-point equations and then present a modulus-based matrix splitting iteration method. We prove the convergence of the proposed method with theorems with the relevant conditions. Our preliminary numerical results show that the method is feasible and effective.

Relaxed Modulus-Based Matrix Splitting Methods for the Linear Complementarity Problem

In this paper, we obtain a new equivalent fixed-point form of the linear complementarity problem by introducing a relaxed matrix and establish a class of relaxed modulus-based matrix splitting iteration methods for solving the linear complementarity problem. Some sufficient conditions for guaranteeing the convergence of relaxed modulus-based matrix splitting iteration methods are presented. Numerical examples are offered to show the efficacy of the proposed methods.

An improved convergence based on accelerated modulus-based Gauss–Seidel method for interactive rigid body simulations

In this paper, we propose a novel method that fits linear complementarity problems arising in interactive rigid-body simulations, based on the accelerated modulus-based Gauss–Seidel (AMGS) method. We give a new sufficient condition for the convergence of the generated sequence under a milder condition on the matrix splitting than the special case of the AMGS method. This gives a flexibility in the choice of the matrix splitting, and an appropriate matrix splitting can lead to a better convergence rate in practice. Numerical experiments show that the proposed method is more efficient than the simple application of the AMGS method, and that the accuracy in each step of the proposed method is superior to that of the projected Gauss–Seidel method.