Research On The Smoothing Method For Several Kinds Of Variational Inequality And Complementarity Problems

Variational inequality and complementarity problems have been widely studied due to their important application value.After decades of development,variational inequality and complementarity problems have made great achievements in the theory research and algorithm.In this paper,on the basis of reading a large number of literature,we focuses on the smoothing method for several kinds of variational inequality and complementarity problems.The main idea is that the variational inequality and complementarity problems are reformulated as a system of equivalent smoothing equations based on a new smoothing function,then algorithm are given.Summed up as follow:(1)We design a new smoothing function of complementary function.Using the function,the KKT-conditions of the box constrained variational inequality problem could be described as a smoothing equations.Then we present the smoothing Newton method.It shows that the algorithm is well-posed and convergence.The numerical experiments are given.(2)On this basis of a new smoothing complementary function,we reformulate the nonlinear complementarity problem as a system of equivalent smoothing equations.We design a smoothing inexact Newton algorithm for solving the nonlinear complementarity problem.Under the suit assumptions,it shows that the algorithm is globally convergent.The numerical experiments are given.(3)The traffic equilibrium problem is reformulated as a stochastic linear complementarity problem.We present a smoothing Newton method of (1 model of the stochastic linear complementarity problem.We also shows that the algorithm is welldefined and global convergence.Numerical experiments indicate that the method is promising.