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Improved Efficiency of the Frank-Wolfe Algorithm for Convex Network Programs

Author

Listed:
  • Larry J. LeBlanc

    (Vanderbilt University, Nashville, Tennessee)

  • Richard V. Helgason

    (Southern Methodist University, Dallas, Texas)

  • David E. Boyce

    (University of Illinois, Urbana, Illinois)

Abstract

We discuss methods for speeding up convergence of the Frank-Wolfe algorithm for solving nonlinear convex programs. Models involving hydraulic networks, road networks and factory-warehouse networks are described. The PARTAN technique and heuristic variations of the Frank-Wolfe algorithm are described which serve to significantly improve the convergence rate with no significant increase in memory requirements. Computational results for large-scale models are reported.

Suggested Citation

  • Larry J. LeBlanc & Richard V. Helgason & David E. Boyce, 1985. "Improved Efficiency of the Frank-Wolfe Algorithm for Convex Network Programs," Transportation Science, INFORMS, vol. 19(4), pages 445-462, November.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:4:p:445-462
    DOI: 10.1287/trsc.19.4.445
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    Cited by:

    1. Maria Daneva & Torbjörn Larsson & Michael Patriksson & Clas Rydergren, 2010. "A comparison of feasible direction methods for the stochastic transportation problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 451-466, July.
    2. A. Ouorou & P. Mahey & J.-Ph. Vial, 2000. "A Survey of Algorithms for Convex Multicommodity Flow Problems," Management Science, INFORMS, vol. 46(1), pages 126-147, January.
    3. 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.
    4. Damberg, Olof & Lundgren, Jan T. & Patriksson, Michael, 1996. "An algorithm for the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 115-131, April.
    5. A. Karakitsiou & A. Migdalas, 2016. "Convex optimization problems in supply chain planning and their solution by a column generation method based on the Frank Wolfe method," Operational Research, Springer, vol. 16(3), pages 401-421, October.
    6. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    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. 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.
    9. Takashi Akamatsu, 2001. "An Efficient Algorithm for Dynamic Traffic Equilibrium Assignment with Queues," Transportation Science, INFORMS, vol. 35(4), pages 389-404, November.
    10. 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.
    11. Yuan, Yun & Yu, Jie, 2018. "Locating transit hubs in a multi-modal transportation network: A cluster-based optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 85-103.
    12. David Di Lorenzo & Alessandro Galligari & Marco Sciandrone, 2015. "A convergent and efficient decomposition method for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 60(1), pages 151-170, January.
    13. Jahn, Olaf & Möhring, Rolf & Schulz, Andreas & Stier Moses, Nicolás, 2004. "System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion," Working papers 4394-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    14. 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.
    15. Jayakrishnan, R. & Tsai, Wei K. & Oh, Jun-Seok & Adler, Jeffrey, 1999. "Event-based ATIS: Practical Implementation and Evaluation of Optimized Strategies (Part I)," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0hz5n8x2, Institute of Transportation Studies, UC Berkeley.

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