报告题目 (Title)：Generalized Nash Equilibrium Problems of Polynomials（多项式广义纳什均衡问题）
报告人 (Speaker)：唐新东（香港浸会大学）
报告时间 (Time)：2024年09月25日(周三) 11：00-15:00
报告地点 (Place)：#腾讯会议：712-500-110
邀请人(Inviter)：周安娃
主办部门：金沙威尼斯欢乐娱人城数学系
报告摘要： We consider generalized Nash equilibrium problems (GNEPs) given by polynomial functions. Based on the Karush-Kuhn-Tucker optimality conditions, we formulate polynomial optimization problems for finding candidate solutions to GNEPs, using Lagrange multiplier expressions. Then, for nonconvex GNEPs, we introduce the feasible extensions to preclude KKT points that are not solutions to the GNEP. Following this sequel, we are able to find a GNE if there exists any, or detect the nonexistence of GNEs. We showed that our approach guarantees to solve the GNEP within finitely many steps under generic assumptions. Particularly, for GNEPs given by quasi-linear constraints, we proposed a new method for finding solutions using partial Lagrange multiplier expressions.
