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Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function

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  • C. Lalitha
  • Mansi Dhingra

Abstract

In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • C. Lalitha & Mansi Dhingra, 2013. "Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function," Journal of Global Optimization, Springer, vol. 57(3), pages 843-861, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:843-861
    DOI: 10.1007/s10898-012-9978-0
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    References listed on IDEAS

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    1. C. Lalitha, 2010. "A new augmented Lagrangian approach to duality and exact penalization," Journal of Global Optimization, Springer, vol. 46(2), pages 233-245, February.
    2. Patrick T. Harker, 1986. "Alternative Models of Spatial Competition," Operations Research, INFORMS, vol. 34(3), pages 410-425, June.
    3. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
    4. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
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