A Hybrid Newton Method For Stochastic Variational Inequality Problems And Its Application

In this thesis,we consider a class of stochastic variational inequality problems.D-ifferent from the classical(deterministic)variational inequality problems,the stochastic variational inequality problems contains a mathematical expectation.Generally,the ex-plicit solution cannot be calculated directly,which increases the difficulty of solving the problems.It is widely used in many fields,such as financial optimization,economics.engineering design,physics and control theory,network flow,etc.For this reason,many algorithms are proposed to solve this kind of problems.We combine the hybrid Newton method of classical variational inequality problems with an unconstrained optimization reformulation based on D-gap function and sample average approximation techniques to present a hybrid Newton methodFirstly,in this thesis,we introduce the origin of stochastic variational inequality problems and its application in many fields.Then we give the application of stochastic approximation and sample average approximation in such problems and give the basic concepts of this thesis.Finally,the main research work of this thesis is briefly introducedSecondly,a hybrid Newton algorithm is proposed for the stochastic variational in-equality problems.Based on the equivalent transformation of the model,the hybrid Newton algorithm for solving the classical variational inequality problems is combined with the D-gap function and the sample average approximation method to construct the hybrid Newton algorithm for solving the stochastic variational inequality problems,and the convergence of the algorithm is proved.The effectiveness of the algorithm is shown by numerical experimentsFinally,considering an important application of stochastic variational inequality problems-traffic equilibrium,we propose a stochastic variational inequality model of traf-fic equilibrium problems,and give two concrete examples of traffic equilibrium.The results of numerical experiments also show that the algorithm proposed in this thesis is feasible and effective.