Research On Numerical Solution Of Nonlinear Complementarity Problem

In recent decades, there are tremendous research achievements on the algorithms of the nonlinear complementarity problem. One of the methods for solving nonlinear complementarity problem is to convert it into an equation, and use the relevant method for solving the equation.This paper presents numerical methods for solving nonlinear complementarity problem. We put this thesis into two parts.Firstly, a new FB-function based on the Po function is given in this paper. The nonlinear complementarity problem is reformulated to the equivalent equations by using the FB-function. A modified smooth Newton method is proposed for solving the nonlinear complementarity problem. Under mild conditions, the global convergence of the algorithm is proved. The numerical experiment shows that the algorithm is potentially efficient.Secondly, this paper describes the fixed point iteration method, differentiable unconstrained optimization method and the interior point method. A new algorithm is proposed on the basis of the existing algorithms and the convergence of the algorithm is analyzed under some suitable assumptions. The numerical results show that the algorithm is feasible.