In this paper we present a simple and practical direct method solving a class ofaffine variational inequalities on rectangle domain. The algorithm is of polynomialtime. And its multiplication work is no more than that of Gauss elimination withpivoting for solving linear system of equations when the variational inequality is alinear complementarity problem.．
We establish a quasi-Newton algorithm for solving a class of variational inequality problems which subproblems are linear equations. By presenting a suitable line search, the algorithm is well-defined. And under certain conditions, we get its global convergence and locally superlinear convergence.
