报告题目 (Title)：Generalized Nash Equilibrium Problems（广义纳什均衡问题）

报告人 (Speaker)：聂家旺 教授 (加州大学圣地亚哥分校)

报告时间：2023年8月2日（周三） 9:00

报告地点：校本部 F309

邀请人：周安娃

主办部门：理学院 数学系

报告摘要： We study generalized Nash equilibrium problems (GNEPs) that are given by polynomial or rational functions. Lagrange multiplier expressions and feasible extensions are introduced to compute generalized Nash equilibria (GNEs). We give a hierarchy of polynomial optimization relaxations to solve the GNEP. The Moment-SOS relaxations are applied to solve the rational optimization problems. Under some genericity assumptions, we show that the proposed hierarchy can compute a GNE if it exists or detect its nonexistence. Numerical experiments are given to show the efficiency of the proposed method.