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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 9, Pages 1447–1454 (Mi zvmmf10779)  

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

Dual methods for finding equilibriums in mixed models of flow distribution in large transportation networks

A. V. Gasnikovab, E. V. Gasnikovac, Yu. E. Nesterovda

a Chair of Mathematical Foundations of Control, Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
b Kharkevich Institute for Information Transmission Problems, Moscow, Russia
c Center for Operation Research and Econometrics Université Catholique de Louvain. Voie du Roman Pays 34, L1.03.01–B-1348 Louvain-la-Neuve (Belgium)
d Department of Big Data and Data Search, Faculty of Computer Science, State University—Higher School of Economics, Moscow, Russia

Abstract: The problem of equilibrium distribution of flows in a transportation network in which a part of edges are characterized by cost functions and the other edges are characterized by their capacity and constant cost for passing through them if there is no congestion is studied. Such models (called mixed models) arise, e.g., in the description of railway cargo transportation. A special case of the mixed model is the family of equilibrium distribution of flows over routes — BMW (Beckmann) model and stable dynamics model. The search for equilibrium in the mixed model is reduced to solving a convex optimization problem. In this paper, the dual problem is constructed that is solved using the mirror descent (dual averaging) algorithm. Two different methods for recovering the solution of the original (primal) problem are described. It is shown that the proposed approaches admit efficient parallelization. The results on the convergence rate of the proposed numerical methods are in agreement with the known lower oracle bounds for this class of problems (up to multiplicative constants).

Key words: primal-dual method, equilibrium distribution of flows in transportation networks, mirror descent method, finding shortest routes.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-31-70001_мол_а_мос
Ministry of Education and Science of the Russian Federation МД 1320.2018.1
Russian Science Foundation 17-11-01027


DOI: https://doi.org/10.31857/S004446690002523-6

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:9, 1395–1403

Bibliographic databases:

UDC: 517.956
Received: 29.12.2016
Revised: 14.11.2017

Citation: A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, “Dual methods for finding equilibriums in mixed models of flow distribution in large transportation networks”, Zh. Vychisl. Mat. Mat. Fiz., 58:9 (2018), 1447–1454; Comput. Math. Math. Phys., 58:9 (2018), 1395–1403

Citation in format AMSBIB
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\paper Dual methods for finding equilibriums in mixed models of flow distribution in large transportation networks
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    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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