A Hybrid Smoothing-Nonsmooth Newton-Type Algorithm Yielding an Exact Solution of the $P_0$-LCP

Abstract

We propose a hybrid smoothing-nonsmooth Newton-type algorithm for solving the $P_0$ linear complementarity problem ($P_0$-$LCP$) based on the techniques used in the non-smooth Newton method and smoothing Newton method. Under some assumptions, the proposed algorithm can find an exact solution of $P_0$-$LCP$ in finite steps. Preliminary numerical results indicate that the proposed algorithm is promising.