Generalized symmetric accelerated over relaxation method for solving absolute value complementarity problems

In this paper, we suggest and analyze a symmetric accelerated over relaxation (SAOR) method for absolute complementarity problems of finding $x\in R^n$, such that $x\geqslant0$, $Ax-|x|-b\geqslant0$, $\langle x,Ax-|x|-b\rangle=0$, where $A\in R^{n\times n}$ and $b\in R^n$. We discuss the convergence of SAOR method when the system matrix $A$ is an $L$-matrix. Several examples are given to illustrate the implementation and efficiency of the method. The results proved in this paper may stimulate further research in this fascinating and interesting field.