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

Jiawang Nie (), Xindong Tang () and Lingling Xu ()
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Jiawang Nie: University of California San Diego
Xindong Tang: University of California San Diego
Lingling Xu: Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University

Computational Optimization and Applications, 2021, vol. 78, issue 2, No 7, 529-557

Abstract: 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.

Keywords: Generalized Nash equilibrium problem; Gauss–Seidel method; Polynomial; Generalized potential game; Moment-SOS hierarchy; 90C30; 91A10; 90C22; 65K05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-020-00242-7

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