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Primal-dual gradient methods for searching network equilibria in combined models with nested choice structure and capacity constraints

Author

Listed:
  • Meruza Kubentayeva

    (Moscow Institute of Physics and Technology)

  • Demyan Yarmoshik

    (Moscow Institute of Physics and Technology)

  • Mikhail Persiianov

    (Moscow Institute of Physics and Technology
    Institute for Information Transmission Problems RAS)

  • Alexey Kroshnin

    (Institute for Information Transmission Problems RAS
    Higher School of Economics)

  • Ekaterina Kotliarova

    (Moscow Institute of Physics and Technology)

  • Nazarii Tupitsa

    (Moscow Institute of Physics and Technology)

  • Dmitry Pasechnyuk

    (Moscow Institute of Physics and Technology)

  • Alexander Gasnikov

    (Moscow Institute of Physics and Technology
    Institute for Information Transmission Problems RAS
    Higher School of Economics)

  • Vladimir Shvetsov

    (Moscow Institute of Physics and Technology
    Russian University of Transport)

  • Leonid Baryshev

    (Russian University of Transport)

  • Alexey Shurupov

    (Russian University of Transport)

Abstract

We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization program. We extend the combined model to the case of the stable dynamics model in the traffic assignment stage, which imposes strict capacity constraints in the network. We propose a way to solve corresponding dual optimization problems with accelerated gradient methods and give theoretical guarantees of their convergence. We conducted numerical experiments with considered optimization methods on Moscow and Berlin networks.

Suggested Citation

  • Meruza Kubentayeva & Demyan Yarmoshik & Mikhail Persiianov & Alexey Kroshnin & Ekaterina Kotliarova & Nazarii Tupitsa & Dmitry Pasechnyuk & Alexander Gasnikov & Vladimir Shvetsov & Leonid Baryshev & A, 2024. "Primal-dual gradient methods for searching network equilibria in combined models with nested choice structure and capacity constraints," Computational Management Science, Springer, vol. 21(1), pages 1-33, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00494-8
    DOI: 10.1007/s10287-023-00494-8
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    References listed on IDEAS

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