The Convergence of Equilibrium Algorithms with Predetermined Step Sizes

Warren B. Powell and Yosef Sheffi
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Warren B. Powell: Massachusetts Institute of Technology, Cambridge, Massachusetts
Yosef Sheffi: Massachusetts Institute of Technology, Cambridge, Massachusetts

Transportation Science, 1982, vol. 16, issue 1, 45-55

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.

Date: 1982
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