An effective method for solving the AVE

Consider Absolute Value Equation (AVE) Ax − |x| − b = 0. The significance of the absolute value equation arises from the fact that linear and quadratic programs, bimatrix games and other problems can all be reduced to the linear complementarity problem that in turn is equivalent to absolute value equation. In this paper, we suggest a parametric uniform approximation method to solve the NP-hard absolute value equation. For this, we uniformly approximate the absolute value in such a way that the nonsmooth absolute value equation can be formulated system of nonlinear eqations. By solving the the parametric smooth system of nonlinear equations using an effective three-step method with five order convergence.