Some Research On The Quasi-Variational Inequality And Its Application In Traffic

Theory of quasi-variational inequalities is the extension of theory of variational inequalities, which is an important part of nonlinear analysis, and widely used in fields of finance, economic, traffic, etc.In this paper, we work on the existence and the uniqueness of solution and algorithms for a class of quasi-variational inequality problems, and the application of quasi-variational inequality problem in traffic. The main ideas in the paper are as following:Section one mainly introduces general condition of quasi-variational inequality problem and the traffic problem relating to flow and environment. Then gives a class of quasi-variational inequality problem and a traffic problem about flow and environment which will be researched in this paper.Section two discusses conditions of existence and uniqueness of solution for this quasi-variational inequality problem, and gives an existence theorem and a uniqueness theorem of solution of quasi-variational inequality problem.Section three gives two algorithms for this quasi-variational inequality problem: projection algorithm and hyperplane projection algorithm.Section four discusses the transformation from the traffic problem about flow and environment to the quasi-variational inequality problem, and gives a relevant numerical experiment.