On the finite termination of the damped-Newton algorithm for linear complementarity problem

Harker and Pang proposed the following open question: whether or not the damped-Newton algorithm for solving the linear complementarity problem is finite if it converges. This paper gives an affirmative answer to this question. Moreover, a new finite termination algorithm for solving general linear complementarity problems is developed to avoid the possibility of the non-convergence of the previous damped-Newton method.