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Convex programming formulations of the asymmetric traffic assignment problem

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  • Hearn, Donald W.
  • Lawphongpanich, Siriphong
  • Nguyen, Sang

Abstract

Recently introduced optimization formulations of the asymmetric traffic assignment problem are developed. The duality of two formulations is shown, and conditions for convexity and differentiability of the objective functions are given. Convexity conditions are also given for the family of formulations recently introduced by Smith (1983). When the travel cost vector is affine and monotone, all of the formulations are shown to be convex programming problems. Algorithmic implications of the results are discussed.

Suggested Citation

  • Hearn, Donald W. & Lawphongpanich, Siriphong & Nguyen, Sang, 1984. "Convex programming formulations of the asymmetric traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 357-365.
    • Handle: RePEc:eee:transb:v:18:y:1984:i:4-5:p:357-365
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    Cited by:

    1. 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.
    2. Hamdouch, Younes & Florian, Michael & Hearn, Donald W. & Lawphongpanich, Siriphong, 2007. "Congestion pricing for multi-modal transportation systems," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 275-291, March.
    3. Xie, Chi & Travis Waller, S., 2012. "Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1023-1042.
    4. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    5. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2020. "Aggregation, disaggregation and decomposition methods in traffic assignment: historical perspectives and new trends," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 199-223.

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