A coordinate descent method for the bi-level O-D matrix adjustment problem

This paper presents a Guass-Seidel type algorithm for the problem of adjusting an O-D matrix by using observed flows in congested networks. The problem is formulated as a bi-level optimization problem. Necessary conditions for some properties of the solution of the O-D matrix adjusting problem are derived and a coordinate descent method is developed. The algorithm takes full advantage of the network structure of the lower level problem and does not require many objective function evaluations. Computational results for some numerical examples are reported.