报告题目：The Matrix Moment–SOS Hierarchy: Convergence Analysis and Tight Relaxations

报告人：黄磊 香港理工大学

报告时间：9月7日 16:00

报告地点：新楼308

摘要：

Polynomial matrix optimization has broad applications in optimal control, matrix optimization, and many other areas, but is generally nonconvex and computationally challenging. The matrix Moment–SOS hierarchy provides a systematic semidefinite framework for solving such problems globally. In this talk, we investigate its convergence properties and tighter variants. We establish finite convergence under generic optimality conditions and the Archimedean assumption. We also derive quantitative degree bounds for matrix Positivstellensatz certificates, leading to an explicit convergence-rate estimate. Finally, we show how to strengthen the hierarchy using first-order optimality conditions and polynomial multiplier expressions.

报告人简介：

黄磊博士现任香港理工大学博士后研究员，曾任美国加州大学圣地亚哥分校数学系访问助理教授。他于2023年获中国科学院数学与系统科学研究院博士学位，2018年获武汉大学学士学位。其研究方向主要包括多项式优化、凸代数几何与半定规划，相关研究成果发表于《Mathematical Programming》《SIAM Journal on Optimization》等国际优化期刊。