A New Proof for Global Convergence of a Smoothing Homotopy Method for the Nonlinear Complementarity Problem

Abstract

In this paper, we propose a new proof for smoothing homotopy method based on the Fischer–Burmeister function to solve the nonlinear complementarity problem under a nonmonotone solution condition. Under this assumption condition imposed on the defined mapping [Formula: see text], global convergence of a smooth curve determined by the referred homotopy equation is established for almost all initial points in [Formula: see text] and it is actually regarded as an interior point method. Besides, if the initial point is expanded to [Formula: see text], the global convergence of the homotopy method is ensured under a similar condition. The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems.