Gauss-Newton Method Algorithm For The Generalized Nonlinear Complementarity Problem

In this paper, we consider the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. First, we reformulate it as a system of smooth nonlinear equations, based on which the damped Gauss-Newton Method algorithm is employed for obtaining its solution, and the convergence analysis are also given in this thesis. Moreover, the numerical experiments are presented.Chapter 1 is mainly an introduction on the generalized nonlinear complementarity problem and the current development on this issue.In chapter 2, the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonlinear equations. And the GNCP is reformulated as unconstrained optimization problem. Based on this reformulation, we first give the conditions under which the stationary point of unconstrained optimization problem is a solution of GNCP, and then give the conditions under which Hessian matrix of vector-valued function is nonsingular. As for the optimization problem, the damped Gauss-Newton Method algorithm is employed for obtaining its solution, and analysis the global convergence of the algorithm, also, the superlinear convergence rate and two order convergence rate of the algorithm is given. Last, we give the numerical experiments.