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

Jiawang Nie*, Xindong Tang, Lingling Xu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)529–557
Number of pages29
JournalComputational Optimization and Applications
Early online date12 Nov 2020
Publication statusPublished - Jan 2021

User-Defined Keywords

  • Generalized Nash equilibrium problem
  • Gauss–Seidel method
  • Polynomial
  • Generalized potential game
  • Moment-SOS hierarchy


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