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Universal Method of Searching for Equilibria and Stochastic Equilibria in Transportation Networks

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Abstract

A universal method of searching for usual and stochastic equilibria in congestion population games is proposed. The Beckmann and stable dynamics models of an equilibrium flow distribution over paths are considered. A search for Nash(–Wardrop) stochastic equilibria leads to entropy-regularized convex optimization problems. Efficient solutions of such problems, more exactly, of their duals are sought by applying a recently proposed universal primal-dual gradient method, which is optimally and adaptively tuned to the smoothness of the problem under study.

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ACKNOWLEDGMENTS

The authors are grateful to Yu.E. Nesterov for his valuable comments.

This work was supported by the Russian Science Foundation (project no. 14-50-00150) (see Sections 4–6), by the Russian Foundation for Basic Research (project no. 15-31-70001-mol_a_mos), and by a grant from the President of the Russian Federation (MK-1806.2017.9) (see Section 4).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, 141700, Dolgoprudnyi, Moscow oblast, Russia

    D. R. Baimurzina, A. V. Gasnikov, E. V. Gasnikova, M. B. Kubentaeva & A. A. Lagunovskaya

  2. Skolkovo Innovation Center, 143026, Moscow, Russia

    D. R. Baimurzina

  3. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, 127051, Moscow, Russia

    A. V. Gasnikov, P. E. Dvurechensky & E. I. Ershov

  4. Weierstrass Institute for Applied Analysis and Stochastics, 410117, Berlin, Germany

    P. E. Dvurechensky

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  1. D. R. Baimurzina
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  2. A. V. Gasnikov
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  3. E. V. Gasnikova
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  4. P. E. Dvurechensky
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  5. E. I. Ershov
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  6. M. B. Kubentaeva
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  7. A. A. Lagunovskaya
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Correspondence to D. R. Baimurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechensky, E. I. Ershov, M. B. Kubentaeva or A. A. Lagunovskaya.

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Translated by I. Ruzanova

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Baimurzina, D.R., Gasnikov, A.V., Gasnikova, E.V. et al. Universal Method of Searching for Equilibria and Stochastic Equilibria in Transportation Networks. Comput. Math. and Math. Phys. 59, 19–33 (2019). https://doi.org/10.1134/S0965542519010020

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