Generalized Nash Equilibrium Problems
of Polynomials
报告专家：唐新东博士（香港浸会大学数学系助理教授）
报告时间：2025年6月6下午4:00-5:00
报告地点：数学学院西202
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.
专家简介：唐新东，香港浸会大学数学系助理教授。2016年本科毕业于四川大学数学基地班，2021年博士毕业于加州大学圣地亚哥分校（UC San Diego）数学系。2021年10月至2023年8月任香港理工大学应用数学系研究助理教授。曾获香港研资局（RGC）优配研究金（GRF）及国家自然科学基金青年项目等资助。现担任《Numerical Algebra, Control, and Optimization》副主编。研究方向为多项式优化、广义纳什均衡、稀疏优化、张量优化及机器人控制等。
邀请人：黄南京
