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A Full Analytical Implementation of the PARTAN/Frank–Wolfe Algorithm for Equilibrium Assignment

Author

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  • Y. Arezki

    (University of Leeds, Leeds LS2 9JT, England)

  • D. Van Vliet

    (University of Leeds, Leeds LS2 9JT, England)

Abstract

We show that an essential step in the PARTAN variant of the Frank–Wolfe algorithm for equilibrium assignment, the calculation of a minimal step length for maintaining feasibility, can be accomplished using either analytical formulas or simple rules.

Suggested Citation

  • Y. Arezki & D. Van Vliet, 1990. "A Full Analytical Implementation of the PARTAN/Frank–Wolfe Algorithm for Equilibrium Assignment," Transportation Science, INFORMS, vol. 24(1), pages 58-62, February.
    • Handle: RePEc:inm:ortrsc:v:24:y:1990:i:1:p:58-62
    DOI: 10.1287/trsc.24.1.58
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    Cited by:

    1. Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
    2. Olaf Jahn & Rolf H. Möhring & Andreas S. Schulz & Nicolás E. Stier-Moses, 2005. "System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion," Operations Research, INFORMS, vol. 53(4), pages 600-616, August.
    3. Taesung Hwang, 2021. "Assignment of Freight Truck Shipment on the U.S. Highway Network," Sustainability, MDPI, vol. 13(11), pages 1-11, June.
    4. 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.
    5. Sang Nguyen & Stefano Pallottino & Federico Malucelli, 2001. "A Modeling Framework for Passenger Assignment on a Transport Network with Timetables," Transportation Science, INFORMS, vol. 35(3), pages 238-249, August.
    6. Oyama, Yuki & Hara, Yusuke & Akamatsu, Takashi, 2022. "Markovian traffic equilibrium assignment based on network generalized extreme value model," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 135-159.
    7. Maria Mitradjieva & Per Olov Lindberg, 2013. "The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment ," Transportation Science, INFORMS, vol. 47(2), pages 280-293, May.
    8. Meruza Kubentayeva & Alexander Gasnikov, 2021. "Finding Equilibria in the Traffic Assignment Problem with Primal-Dual Gradient Methods for Stable Dynamics Model and Beckmann Model," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    9. Marta Rojo, 2020. "Evaluation of Traffic Assignment Models through Simulation," Sustainability, MDPI, vol. 12(14), pages 1-19, July.

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