The Application of Variational Inequality with Separable Structure and Special Constraints in a traffic Assignment Problem

Recently, some modified alternating direction methods have been proposed to solve a class of nonlinear variational inequality problem with separable structure. These methods are more efficient than the classical one, but cannot avoid solving a variational inequality subproblem. In this paper, we convert the nonlinear variational inequality problems with separable structure and special constraints to an equivalent cobweb model, and then we propose a self-adaptive bisection method to solve the original problems. Specifically, the proposed method only needs to compute some iterative values which are not needed to solve a variational inequality subproblem. The proposed algorithm is applied to the traffic assignment problem, and the results show that the proposed algorithm is quite robust with respect to different starting points as well as different inner loop accuracy.