An Approximation Of The Chance Constrained Variational Inequality Problems

Stochastic variational inequality problem is a hot topic in the field of stochastic programming,which has been widely used in the fields of economy,information and engineering.Chance-constrained stochastic variational inequality models have attracted much attention because of the uncertainty of the parameters involved.Chance constrained optimization model has attracted the research of scholars at home and abroad since it was proposed.This kind of model is usually non-convex and non-smooth,so there are many difficulties in numerical calculation.Many approximate solving algorithms have been proposed in the literature,such as convex approximation method,D.C.Approximation method,smooth approximation method,etc.In this paper,we mainly discuss the approximate method of solving the chance constrained stochastic variational inequality.Specific research results are as follows:In the first chapter,the research background of stochastic variational inequality and chance constrained optimization problems is summarized,and some relevant preliminary knowledge is given.The second chapter introduces the reconstruction models of the variational inequality problem,including the deterministic model and the random variational inequality model,and analyzes the effective solutions of different models.In the third chapter,the problem of chance-constrained stochastic variational inequality is discussed.Firstly,a stochastic variational inequality model with chance constraints is constructed,and an equivalent model of stochastic variational inequality with chance constraints on a specific set is given.Secondly,an approximate continuous function of the characteristic function is constructed,and the properties of the approximate function are discussed.Finally,the corresponding approximation problem is established and the convergence analysis is carried out.In chapter 4,we study the approximate method of solving the chance constrained stochastic variational inequality problem.Firstly,the approximation problem of chance constrained stochastic variational inequality is constructed based on the approximation function.Secondly,the sample average approximation function of the chance constraint function is constructed,and the corresponding sample average approximation problem is established,which is transformed into an unconstrained minimization problem.Finally,combined with a specific example,the random generator Unifrnd is used to generate independent samples of the same distribution,and the MATLAB program is used to solve the problem.The calculation results show that the solution of the sample average approximate problem is the approximate solution of the stochastic variational inequality.