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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 1, Pages 21–36
DOI: https://doi.org/10.1134/S0044466919010022 (Mi zvmmf10814) 		 
This article is cited in 15 scientific papers (total in 15 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
Citations (15)
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DOI: https://doi.org/10.1134/S0044466919010022
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).
Received: 19.01.2017
Revised: 04.12.2017
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 1, Pages 19–33
DOI: https://doi.org/10.1134/S0965542519010020
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
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
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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