论文标题
多项式的通用纳什均衡问题的高斯 - 西德尔方法
The Gauss-Seidel Method for Generalized Nash Equilibrium Problems of Polynomials
论文作者
论文摘要
本文涉及多项式（GNEPP）的普遍纳什均衡问题。我们应用高斯seidel方法和套管型矩弛豫式松弛来解决gnepps。高斯 - 西德尔方法的收敛性以某些特殊的GNEPPS（例如广义潜在游戏（GPG））而闻名。我们为GPG提供了足够的条件，并根据Putinar的Potitivstellensatz提出了数值证书。给出了凸面和非凸面gnepps的数值示例，以证明该方法的效率。
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.
