Newton Method vs. Semismooth Newton Method for Singular Solutions of Nonlinear Complementarity Problems

Abstract

Among the most successful techniques for solving nonlinear complementarity problems is the one consisting of reformulation of the problem in question as a system of nonlinear equations, by means of the so-called complementarity functions. Different complementarity functions lead to nonlinear systems with different smoothness and regularity properties, thus allowing for application of different classed of numerical methods. In this paper we compare the Newton method for the smooth reformulation with the semismooth Newton method for the reformulation relying on the nonsmooth Fischer--Burmeister complementarity function, with a special emphasis on the cases when the solution in question violates the strict complementarity condition.