The Gauss-Seidel Method for Generalized Nash Equilibrium Problems of Polynomials
Jiawang Nie, Xindong Tang, Lingling Xu
TL;DR
This paper introduces a method combining the Gauss-Seidel approach and Moment-SOS relaxations to solve polynomial generalized Nash equilibrium problems, providing convergence conditions and numerical validation.
Contribution
It develops a novel framework applying Gauss-Seidel and Moment-SOS relaxations to GNEPPs, with convergence analysis and practical numerical examples.
Findings
Effective solution method for GNEPPs demonstrated
Convergence conditions established for GPGs
Numerical examples show efficiency for convex and nonconvex cases
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.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Optimization and Variational Analysis · Matrix Theory and Algorithms