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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 1, Pages 21–36 (Mi zvmmf10814)  

This article is cited in 2 scientific papers (total in 2 papers)

Universal method of searching for equilibria and stochastic equilibria in transportation networks

D. R. Baymurzinaab, A. V. Gasnikovac, E. V. Gasnikovaa, P. E. Dvurechenskiicd, E. I. Ershovc, M. B. Kubentayevaa, A. A. Lagunovskayaa

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia
b Skolkovo Innovation Center, Moscow, 143026 Russia
c Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051 Russia
d 10117 Berlin, Mohrenstr, 39, WIAAS, Germany

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.

Key words: transportation flows, transportation networks, universal method of similar triangles, dual problem, Beckmann’s model, stable dynamics model.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
Russian Foundation for Basic Research 15-31-70001
Ministry of Education and Science of the Russian Federation МК-1806.2017.9
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).

DOI: https://doi.org/10.1134/S0044466919010022

English version:
Computational Mathematics and Mathematical Physics, 2019, 59:1, 19–33

Bibliographic databases:

UDC: 519.626
Received: 19.01.2017
Revised: 04.12.2017

Citation: D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Universal method of searching for equilibria and stochastic equilibria in transportation networks”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 21–36; Comput. Math. Math. Phys., 59:1 (2019), 19–33

Citation in format AMSBIB
\by D.~R.~Baymurzina, A.~V.~Gasnikov, E.~V.~Gasnikova, P.~E.~Dvurechenskii, E.~I.~Ershov, M.~B.~Kubentayeva, A.~A.~Lagunovskaya
\paper Universal method of searching for equilibria and stochastic equilibria in transportation networks
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
\vol 59
\issue 1
\pages 21--36
\jour Comput. Math. Math. Phys.
\yr 2019
\vol 59
\issue 1
\pages 19--33

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    This publication is cited in the following articles:
    1. A. I. Tyurin, “Pryamo-dvoistvennyi bystryi gradientnyi metod s modelyu”, Kompyuternye issledovaniya i modelirovanie, 12:2 (2020), 263–274  mathnet  crossref
    2. E. V. Kotlyarova, A. V. Gasnikov, E. V. Gasnikova, D. V. Yarmoshik, “Poisk ravnovesii v dvukhstadiinykh modelyakh raspredeleniya transportnykh potokov po seti”, Kompyuternye issledovaniya i modelirovanie, 13:2 (2021), 365–379  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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