Convex generalized Nash equilibrium problems and polynomial optimization

• 成果类型: Article
• 署名作者: Nie, Jiawang; Tang, Xindong
• 署名单位: University of California System; University of California San Diego; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01739-7
• 发表日期: 2023
• 页码: 1485-1518
• 关键词: Hierarchy; games

摘要

This paper studies convex generalized Nash equilibrium problems that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formulate efficient polynomial optimization for computing generalized Nash equilibria (GNEs). The Moment-SOS hierarchy of semidefinite relaxations are used to solve the polynomial optimization. Under some general assumptions, we prove the method can find a GNE if there exists one, or detect nonexistence of GNEs. Numerical experiments are presented to show the efficiency of the method.