On the convergence of modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems with H+-matrices

摘要

A class of modulus-based iteration methods for the nonlinear complementarity problem are presented by reformulating the complementarity problem to an implicit fixed-point equation. In order to efficiently implement these methods, practical iteration schemes based on matrix splitting and the choices of the parameters are presented and well studied. Moreover, we extend the convergence theory from the H-compatible splitting to H-splitting when the matrix is an H+-matrix, which results in more choices for the parameters. Numerical experiments are given to verify the theoretical results and illustrate the efficiency of the proposed methods.