报告题目 (Title)：Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations（矩阵多项式优化的拉格朗日乘子表达与紧松弛）
报告人 (Speaker)：聂家旺 教授（加州大学圣地亚哥分校）
报告时间 (Time)：2025年12月16日（周二）15:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：周安娃
主办部门：理学院数学系
报告摘要：This talk discusses matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under the nondegeneracy condition. Using Lagrange multiplier matrix expressions, we propose a strengthened Moment-SOS hierarchy for solving matrix polynomial optimization. Under some general assumptions, we show that this strengthened hierarchy is tight, or equivalently, it has finite convergence. We also study how to detect tightness and how to extract optimizers. Numerical experiments are provided to show the efficiency of the strengthened hierarchy.
