(1) Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Buonarroti 12, 00185 Roma, Italy;(2) Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany
Abstract:
In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on
a semismooth equation reformulation of the complementarity problem. We exploit the recent extension of Newton's method to
semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously
differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild
assumptions. Other interesting features of the new algorithm are an extreme simplicity along with a low computational burden
per iteration. We include numerical tests which show the viability of the approach.