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The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials

Author

Listed:
  • Jiawang Nie

    (University of California San Diego)

  • Xindong Tang

    (University of California San Diego)

  • Lingling Xu

    (Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University)

Abstract

This paper concerns the generalized Nash equilibrium problem of polynomials (GNEPP). We apply the Gauss–Seidel method and Moment-SOS relaxations to solve GNEPPs. The convergence of the Gauss–Seidel method is known for some special GNEPPs, such as generalized potential games (GPGs). We give a sufficient condition for GPGs and propose a numerical certificate, based on Putinar’s Positivstellensatz. Numerical examples for both convex and nonconvex GNEPPs are given for demonstrating the efficiency of the proposed method.

Suggested Citation

  • Jiawang Nie & Xindong Tang & Lingling Xu, 2021. "The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials," Computational Optimization and Applications, Springer, vol. 78(2), pages 529-557, March.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:2:d:10.1007_s10589-020-00242-7
    DOI: 10.1007/s10589-020-00242-7
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