Regularized Smoothing Approximation Of Linear Complementarity Problems

In this paper we study a regularized smoothing approximation of the linear complementarity problem(LCP for short),where we approximate the LCP by a nonlinear differentiable algebraic equation(with parameters),such an equation has a unique solution and can be numerically well treated by the existing solvers.We show the convergence of the approximation: the unique solution of the algebraic equation is convergent to the solution of the LCP when the regularization and the smoothing parameters go to zero,and the limit gives the least norm solution of the LCP if the smoothing parameter goes to zero faster than the other one.Numerical experiments are performed,the results support the convergence nature of the proposed method.