| Mixed variational inequalities can be used to describe a wide range of issues that arise in disciplines including mechanics,control,economics,social sciences and so on.It is worth noting that more mathematical models must be established in order to account for the complexity of practical problems by introducing the restrictions of sub-problems that can reflect more general problems.These models are frequently referred to as bilevel programming model.Bilevel mixed variational inequalities,as one of the main contents of the bilevel programming problems,have important research significance.This dissertation mainly employs the dynamic system method to solve the bilevel mixed variational inequality problems,and the main results of this dissertation can be summarized as follows:1.Our focus is on a class of bilevel mixed variational inequality problems in Hilbert spaces.Since the existence of mixed terms,the classical projection algorithm commonly used to solve variational inequality problems is no longer holds.Hence,we use the generalized f-projection and a continuous algorithm known as the dynamic system method to solve the bilevel mixed variational inequality problems.Under some conditions,we prove that the solution of the dynamic system method strongly converges to the unique solution of the bilevel mixed variational inequality.2.We mainly discuss the Levitin-Polyak(LP)well posedness by perturbations of a class of bilevel mixed vector variational inequality problems in Banach spaces.Firstly,we introduce the concepts of the LP well-posedness by perturbations and the generalized LP wellposedness by perturbations for bilevel mixed vector variational inequality problems.Additionally,we demonstrate that the LP well-posedness by perturbations of the bilevel mixed vector variational inequality problems is equivalent to the uniqueness of the solution of the original problem,and that the generalized LP well-posedness by perturbations is equivalent to the nonemptiness and boundedness of the solution set of the original problem. |
