Sample Average Approximation Method For Stochastic Variational Inequality Problems

Variational inequality plays a vital role in transportation,computing,electric pow-er.machinery.finance and energy source.Many equilibrium problems can be solved by variational inequalities theory. From the1960s of the20th century to recently,the theory of deterministic variational inequality becomes more and more mature,which has become a very fruitful disciplines in the field of mathematical programming.But in our daily life there often encounter a lot of stochastic uncertainties which make important impact on some results such as weather,hobbies,needs and so on.So it boosts the research of stochas-tic variational inequality.The main content is organized as following:In the second chapter, it introduces some useful prerequisites including the defini-tion and theorems of variational inequalities,some basic definitions and properties of the projection,related definitions of stochastic variational inequality and the sample average approximation method for stochastic variational inequality and its applications.In the third chapter, Some typical algorithms for solving variational inequality have been introduced and the algorithms we will use in the following chapter have been intro-duced thoroughly.In the fourth chapter, we make use of integral deviation to analysis the convergence of the solutions of the SAA problem to the solutions of the true problem.Then,we use the projection and contraction algorithm to solve the strong monotone stochastic variational inequalities and use the damped Newton algorithm to solve the monotone stochastic vari-ational inequalities and non-monotone stochastic variational inequalities.Lastly,we make a simple analysis of the numerical results.