Geodesic
Numerical methods for the problem of traffic flow equilibrium in the Beckmann and the stable dynamic models
Matematičeskoe modelirovanie, Tome 28 (2016) no. 10, pp. 40-64

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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.
Keywords: equilibrium transportation models, Nash–Wardrop equilibrium, Beckmann's model, Stable Dynamic model, Frank–Wolfe algorithm, Mirror descent algorithm, dual averaging, randomization, randomized component gradient descent algorithm. 
@article{MM_2016_28_10_a3,
     author = {A. V. Gasnikov and P. E. Dvurechensky and Yu. V. Dorn and Yu. V. Maksimov},
     title = {Numerical methods for the problem of traffic flow equilibrium in the {Beckmann} and the stable dynamic models},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {40--64},
     publisher = {mathdoc},
     volume = {28},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_10_a3/}
}
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A. V. Gasnikov; P. E. Dvurechensky; Yu. V. Dorn; Yu. V. Maksimov. Numerical methods for the problem of traffic flow equilibrium in the Beckmann and the stable dynamic models. Matematičeskoe modelirovanie, Tome 28 (2016) no. 10, pp. 40-64. http://geodesic.mathdoc.fr/item/MM_2016_28_10_a3/