On the Finite Termination of an Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems

By using a smooth entropy function to approximate the non-smooth max-type function, a verticallinear complementarity problem (VLCP) can be treated as a family of parameterized smoothequations. A Newton-type method with a testing procedure is proposed to solve sucha system. We show that the proposed algorithm finds an exact solution of VLCP in a finitenumber of iterations, under some conditions milder than those assumed in literature. Somecomputational results are included to illustrate the potential of this approach