Solution And Convergence Analysis Of A Class Of Stochastic Vector Variational Inequality Problems

Vector variational inequality(VVI)is an e?ective tool to solve vector optimization problems,which is extensively used in the study of tra c network equilibrium,market equilibrium and so on.As a matter of fact,in many cases,the actual issues may contain uncertain factors.Consequently,it is interesting and meaningful to study the stochastic version of VVI(SVVI).In this dissertation,we mainly consider a class of stochastic vector variational inequality problems in finite-dimensional Euclidean spaces.The main results of this dissertation can be summarized as follows:1.Our focus on the SVVI problem by the weighted expected residual minimization(WERM)method.The SVVI is reformulated as a deterministic model with simple constraint,i.e.,WERM problem.Then,the properties of the WERM problem are investigated,including the continuous di?erentiability of the objective function and some results,such as the global error bound and the boundedness of the level set.Since the distribution of random variables and the expectation of objective function in the WERM formulation are mostly unknown,it is di cult to get an accurate solution to the original problem.A sample average approximation(SAA)method is utilized to solve the WERM problem.Furthermore,convergence and exponential convergence rate of global optimal solutions for approximation problem,as well as the convergence of stationary points are analyzed,respectively.These results generalize some recent results about SVI problems and improve the main results of SVVI considered by Zhao et al.2.The SVVI problem is reformulated as a deterministic model,i.e.,UERM problem,by employing the unconstrained ERM(UERM)method.Then,the properties of the objective function are investigated and a sample average approximation method is proposed for solving the UERM problem.Convergence of approximation problem for global optimal solutions and stationary points is analyzed,respectively.These results generalize some recent results about SVI and stochastic complementary problems and improve the main results of SVVI considered by Zhao et al.from constrained cases to unconstrained cases.