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A Nonlinear Equation Framework for Solving Network Equilibrium Problems

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  • C Fisk

    (Department of Civil Engineering, University of Illinois, Urbana, IL 61801, USA)

Abstract

The author presents a general framework for formulating network equilibrium problems in which the equilibrium conditions are given by a system of nonlinear equations. Existence and uniqueness results are presented, and iterative solution techniques with well-defined convergence properties are suggested. For illustrative purposes, these techniques are applied to a specific two-mode equilibrium model; a discussion comparing some aspects of this approach with other existing approaches is included.

Suggested Citation

  • C Fisk, 1984. "A Nonlinear Equation Framework for Solving Network Equilibrium Problems," Environment and Planning A, , vol. 16(1), pages 67-80, January.
    • Handle: RePEc:sae:envira:v:16:y:1984:i:1:p:67-80
    DOI: 10.1068/a160067
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    References listed on IDEAS

    as
    1. Michael Florian, 1977. "A Traffic Equilibrium Model of Travel by Car and Public Transit Modes," Transportation Science, INFORMS, vol. 11(2), pages 166-179, May.
    2. Caroline Fisk & Sang Nguyen, 1982. "Solution Algorithms for Network Equilibrium Models with Asymmetric User Costs," Transportation Science, INFORMS, vol. 16(3), pages 361-381, August.
    3. Michael A. Hall, 1978. "Properties of the Equilibrium State in Transportation Networks," Transportation Science, INFORMS, vol. 12(3), pages 208-216, August.
    4. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    5. C. S. Fisk & D. E. Boyce, 1983. "Alternative Variational Inequality Formulations of the Network Equilibrium-Travel Choice Problem," Transportation Science, INFORMS, vol. 17(4), pages 454-463, November.
    6. Michael Florian & Heinz Spiess, 1983. "On Binary Mode Choice/Assignment Models," Transportation Science, INFORMS, vol. 17(1), pages 32-47, February.
    7. Mustafa Abdulaal & Larry J. LeBlanc, 1979. "Methods for Combining Modal Split and Equilibrium Assignment Models," Transportation Science, INFORMS, vol. 13(4), pages 292-314, November.
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