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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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    1. 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.
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    3. 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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    5. N. Yamashita, 1998. "Properties of Restricted NCP Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 701-717, September.
    6. L. Brasco & G. Carlier, 2013. "Congested Traffic Equilibria and Degenerate Anisotropic PDEs," Dynamic Games and Applications, Springer, vol. 3(4), pages 508-522, December.
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