Rondom Variational Inequality And Its Application

The random variational inequality theory is an important component of the random functional analysis and has been widely applied to mathematics, economics, mechanics and control theory, etc. It is one of hot problems paid close attention by scholars in the field of probability and statistics. This theory plays an important role in promoting to random functional analysis and application of the theory, and will also provide a powerful tool for all kinds of random equations and random control problems. The research for it has important learning value.This paper studies systematically the problem of random variational inequality from the theory, algorithms and applications. The received results are a unity and extension of a large number of known results, and the question this article discussed contains certain existing variation inequalities as the exceptional case. First, this paper introduces the development history of variational inequalities and some basic concepts the research process used. Second, projection algorithm, the auxiliary principle and the resolvent equation method are separately used to study the random generalized set-valued strongly nonlinear mixed variational inequality, the random generalized set-valued mixed quasi-variational inequality and the random mixed variational-like inequality. We discuss their existence of solutions, and give a number of relatively new iterative algorithms. Furthermore, the convergence of the new algorithms is proved. At last, this article connects the variational inequality theory with the theory of probability and statistics, for the characteristics of Chinese urban mixed traffic network, taking the elementary theory of transportation choice behavior in the mixed traffic network as a foundation, the random variational inequality model of traffic distribution is proposed. At the same time, we establish bi-level programming model to solve the optimization problems of urban mixed traffic network system. Not only in theory, we prove that this bi-level programming model is reasonable, and its solution algorithm is designed.