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Inexact Newton Method for Solving Generalized Nash Equilibrium Problems

Author

Listed:
  • Abhishek Singh

    (Indian Institute of Technology (Banaras Hindu University))

  • Debdas Ghosh

    (Indian Institute of Technology (Banaras Hindu University))

  • Qamrul Hasan Ansari

    (Aligarh Muslim University
    College of Sciences, Chongqing University of Technology)

Abstract

In this article, we present an inexact Newton method to solve generalized Nash equilibrium problems (GNEPs). Two types of GNEPs are studied: player convex and jointly convex. We reformulate the GNEP into an unconstrained optimization problem using a complementarity function and solve it by the proposed method. It is found that the proposed numerical scheme has the global convergence property for both types of GNEPs. The strong BD-regularity assumption for the reformulated system of GNEP plays a crucial role in global convergence. In fact, the strong BD-regularity assumption and a suitable choice of a forcing sequence expedite the inexact Newton method to Q-quadratic convergence. The efficiency of the proposed numerical scheme is shown for a collection of problems, including the realistic internet switching problem, where selfish users generate traffic. A comparison of the proposed method with the existing semi-smooth Newton method II for GNEP is provided, which indicates that the proposed scheme is more efficient.

Suggested Citation

  • Abhishek Singh & Debdas Ghosh & Qamrul Hasan Ansari, 2024. "Inexact Newton Method for Solving Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1333-1363, June.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:3:d:10.1007_s10957-024-02411-8
    DOI: 10.1007/s10957-024-02411-8
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    References listed on IDEAS

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