A Class Of Separable Variational Inequalities With Linear Constraints And Application

Variational inequality problem originated from the classical variational calculus, it has contacted with fixed point theory, equilibrium problem, complementarity problem and optimization problem closely. And it is widely used in different fields, such as traffic equilibrium, network economics, engineering optimization and regional science. Particularly, separable variational inequality problem with linear constraints and people’s real life are closely linked.This paper mainly discusses the separable variational inequality problem with linear constraints. A new iterative algorithm is proposed for this problem, and its global convergence is proved, in addition, we verify its effectiveness by numerical experiment. Finally, we put the above theory applied to the stochastic traffic equilibrium problem.Specific content as follows:In chapter one, we outline the background and current situation of variational inequality problem, especially the separable variational inequalities with linear constraints. Then present the background of stochastic traffic equilibrium and the required knowledge.In chapter two, inspired that the structured variational inequality can be solved by the logarithmic-quadratic proximal method quickly, and considering that the alternating direction method is difficult to find the result of sub-variational inequaliti-es, we put forward a new alternating direction method. Then we prove its global convergence, and with the support of numerical experiment, we verify its effectivene-ss.In chapter three, as the particularity of variational inequality problem with linear constraints, for a kind of stochastic traffic equilibrium problems which are with fixed demand and capacity constraints, we construct a corresponding variational inequality model.In chapter four, we make a summary of the full text and give prospects.