English

The Gauss-Seidel Method for Generalized Nash Equilibrium Problems of Polynomials

Optimization and Control 2020-09-08 v1

Abstract

This paper concerns the generalized Nash equilibrium problem of polynomials (GNEPP). We apply the Gauss-Seidel method and Lasserre type 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.

Cite

@article{arxiv.2009.02809,
  title  = {The Gauss-Seidel Method for Generalized Nash Equilibrium Problems of Polynomials},
  author = {Jiawang Nie and Xindong Tang and Lingling Xu},
  journal= {arXiv preprint arXiv:2009.02809},
  year   = {2020}
}

Comments

24 pages

R2 v1 2026-06-23T18:20:52.906Z