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Approximation of the steepest descent direction for the O-D matrix adjustment problem

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  • Esteve Codina
  • Lídia Montero

Abstract

In this paper, a method to approximate the directions of Clarke's generalized gradient of the upper level function for the demand adjustment problem on traffic networks is presented. Its consistency is analyzed in detail. The theoretical background on which this method relies is the known property of proximal subgradients of approximating subgradients of proximal bounded and lower semicountinuous functions using the Moreau envelopes. A double penalty approach is employed to approximate the proximal subgradients provided by these envelopes. An algorithm based on partial linearization is used to solve the resulting nonconvex problem that approximates the Moreau envelopes, and a method to verify the accuracy of the approximation to the steepest descent direction at points of differentiability is developed, so it may be used as a suitable stopping criterion. Finally, a set of experiments with test problems are presented, illustrating the approximation of the solutions to a steepest descent direction evaluated numerically. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Esteve Codina & Lídia Montero, 2006. "Approximation of the steepest descent direction for the O-D matrix adjustment problem," Annals of Operations Research, Springer, vol. 144(1), pages 329-362, April.
    • Handle: RePEc:spr:annopr:v:144:y:2006:i:1:p:329-362:10.1007/s10479-006-0007-x
    DOI: 10.1007/s10479-006-0007-x
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    References listed on IDEAS

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    Cited by:

    1. S. Dempe & A. Zemkoho, 2012. "Bilevel road pricing: theoretical analysis and optimality conditions," Annals of Operations Research, Springer, vol. 196(1), pages 223-240, July.
    2. Garcia-Rodenas, Ricardo & Verastegui-Rayo, Doroteo, 2008. "A column generation algorithm for the estimation of origin-destination matrices in congested traffic networks," European Journal of Operational Research, Elsevier, vol. 184(3), pages 860-878, February.
    3. Walpen, Jorgelina & Mancinelli, Elina M. & Lotito, Pablo A., 2015. "A heuristic for the OD matrix adjustment problem in a congested transport network," European Journal of Operational Research, Elsevier, vol. 242(3), pages 807-819.

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