Convex generalized Nash equilibrium problems and polynomial optimization

Jiawang Nie*, Xindong Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


This paper studies convex generalized Nash equilibrium problems that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formulate efficient polynomial optimization for computing generalized Nash equilibria (GNEs). The Moment-SOS hierarchy of semidefinite relaxations are used to solve the polynomial optimization. Under some general assumptions, we prove the method can find a GNE if there exists one, or detect nonexistence of GNEs. Numerical experiments are presented to show the efficiency of the method.

Original languageEnglish
Pages (from-to)1485-1518
Number of pages34
JournalMathematical Programming
Early online date7 Dec 2021
Publication statusPublished - Apr 2023

Scopus Subject Areas

  • Software
  • Mathematics(all)

User-Defined Keywords

  • Generalized Nash equilibrium problem
  • Convex polynomial
  • Polynomial optimization
  • Moment-SOS relaxation
  • Lagrange multiplier expression


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