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The Convergence of Equilibrium Algorithms with Predetermined Step Sizes

Author

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  • Warren B. Powell

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Yosef Sheffi

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

The focus of this paper is on a certain class of equilibrium traffic assignment problems characterized by a path formulation of the associated mathematical programs. In such cases the equilibration iterations would require path enumeration, and are therefore prohibitively expensive. In this paper we prove that a predetermined sequence of step sizes (in a descent direction) would guarantee, under certain regularity conditions, convergence to the equilibrium solution. This algorithm was suggested in the literature without a proof of convergence, which we give here.

Suggested Citation

  • Warren B. Powell & Yosef Sheffi, 1982. "The Convergence of Equilibrium Algorithms with Predetermined Step Sizes," Transportation Science, INFORMS, vol. 16(1), pages 45-55, February.
    • Handle: RePEc:inm:ortrsc:v:16:y:1982:i:1:p:45-55
    DOI: 10.1287/trsc.16.1.45
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