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A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium

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  • Azam Asanjarani

    (The University of Auckland)

Abstract

We consider a geometrical approach to the optimisation problems motivated by transportation system management. Here, we provide a comprehensive account of geometric programming based on the elementary Finsler geometry in $${\mathbb {R}}^n$$ R n . Then, we present a Finslerian dynamical model for the nonlinear complementarity problem of traffic equilibrium that can be applied to a variety of equilibrium problems.

Suggested Citation

  • Azam Asanjarani, 2023. "A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 797-809, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-023-02162-y
    DOI: 10.1007/s10957-023-02162-y
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    References listed on IDEAS

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    3. Liqun Qi, 1999. "Regular Pseudo-Smooth NCP and BVIP Functions and Globally and Quadratically Convergent Generalized Newton Methods for Complementarity and Variational Inequality Problems," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 440-471, May.
    4. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    5. C. Kanzow & N. Yamashita & M. Fukushima, 1997. "New NCP-Functions and Their Properties," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 115-135, July.
    6. Houyuan Jiang, 1999. "Global Convergence Analysis of the Generalized Newton and Gauss-Newton Methods of the Fischer-Burmeister Equation for the Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 529-543, August.
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