Rational generalized nash equilibrium problems

Jiawang Nie, Xindong Tang, Suhan Zhong

Research output: Contribution to journalJournal articlepeer-review


This paper studies generalized Nash equilibrium problems that are given by rational functions. The optimization problems are not assumed to be convex. Rational expressions for Lagrange multipliers and feasible extensions of KKT points are introduced to compute a generalized Nash equilibrium (GNE). We give a hierarchy of rational optimization problems to solve rational generalized Nash equilibrium problems. The existence and computation of feasible extensions are studied. The Moment-SOS relaxations are applied to solve the rational optimization problems. Under some general assumptions, we show that the proposed hierarchy can compute a GNE if it exists or detect its nonexistence. Numerical experiments are given to show the efficiency of the proposed method.

Original languageEnglish
Pages (from-to)1587-1620
Number of pages34
JournalSIAM Journal on Optimization
Issue number3
Publication statusPublished - Jun 2023

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Applied Mathematics

User-Defined Keywords

  • generalized Nash equilibrium
  • rational function
  • feasible extension
  • Lagrange multiplier expression
  • Moment-SOS relaxation


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