报告题目：On the exactness of Lasserre’s relaxation for polynomial optimization with equality constraints
报 告 人：瞿铮（香港大学）
会议时间：2022/3/22 9:00开始
会议地点：腾讯会议，会议号：843696675
报告摘要：We study exactness condition for Lasserre’s relaxation method for polynomial optimization problem with n variables under equality constraints defined by n polynomials. Under the assumption that the quotient ring has dimension equal to the product of the degrees of the n equality defining polynomials, we obtain an explicit bound on the order of Lasserre’s relaxation which guarantees exactness. When the common zero locus are real and all of multiplicity one, we describe the exact region as the convex hull of the moment map image of a vector subspace. For the relaxation of order equal to the explicit bound minus one, the convex hull coincides with the moment map image, and is diffeomorphic to its amoeba. Based on the theory of amoeba, we obtain an explicit description of the exact region, from which we further derive error estimations for relaxation of this specific order.
报告人简介：瞿铮，2013年于法国巴黎综合理工大学获得博士学位，2014年在英国爱丁堡大学担任博士后。2015年起在香港大学任助理教授。瞿铮的主要研究方向为大规模优化和控制问题的数值求解，文章发表在Journal of Differential Equation, SIAM Jounal on Control and Optimization, Mathematical Programming Computation, IMA Jounal of Numerical Analysis, Computational Optimizaiton and Applications, Optimization Methods and Software 等期刊上。
