Numerical methods for the problem of traffic flow equilibrium in the Beckmann and the stable dynamic models

In this work we propose new computational methods for transportation equilibrium problems. For Beckmann's equilibrium model we consider Frank–Wolfe algorithm in a view of modern complexity results for this method. For Stable Dynamic model we propose new methods. First approach based on mirror descent scheme with Euclidean prox-structure for dual problem and randomization of a sum trick. Second approach based on Nesterov's smoothing technique of dual problem in form of Dorn–Nesterov and new implementation of randomized block-component gradient descent algorithm.