Research On Inexact Smoothing Method For Nonlinear Complementarity Problems

The solution of complementarity problem is an important part of mathematical programming.In real life,complementarity problem is the core problem in many fields such as economy,transportation,production.In this thesis,we study the nonlinear complementarity problem based on the existing algorithms,it show that the computational efficiency of the algorithm is improved obviously.The numerical results presented are valid under each proposed algorithm.Firstly,the methods and basic theory are introduced,some usually approximation functions are given.In the second chapter,we put forward the new inexact smoothing algorithm based on smoothing approximation function.Under appropriate conditions,the global convergence and local superlinear convergence of the algorithm are built.The numerical experiments showed that the algorithm is effective.In the third chapter,we propose an inexact Levenberg-Marquardt method based on given function approximation.We prove the global convergence of the algorithm.We compare the numerical results of the algorithm under different parameters,so we get the better parameters for the algorithmIn the fourth chapter,the above algorithm is invalid when the Jacobi matrix is singular,so a modified Levenberg-Marquardt method based on the Levenberg-Marquardt algorithm is given.Under the appropriate conditions,the convergence of the algorithm is proved.The modified algorithm is feasible and effective for solving most complementarity problems.