理学论坛第二百二十二次学术活动(夏勇报告)

发布时间:2024-03-20浏览次数:10

报告题目:Linear Programming on the Stiefel Manifold

报告人:夏勇

报告人单位:北京航空航天大学

时间:2024年03月22日(星期五),下午15:00

地点:仙林校区教2-327会议室

主办单位:yl60000永利官网

邀请人:王友国

报告内容:

Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all p-tuples of orthonormal vectors in R^n satisfying k additional linear constraints. Despite the classical polynomial-time solvable case k=0, general (LPS) is NP-hard. According to the Shapiro-Barvinok-Pataki theorem, (LPS) admits an exact semidefinite programming relaxation when p(p+1)/2<=n-k, which is tight when p=1. Surprisingly, we can greatly strengthen this sufficient exactness condition to p<=n-k, which covers the classical case p<=n and k=0. Regarding (LPS) as a smooth nonlinear programming problem,we reveal a nice property that under the linear independence constraint qualification, the standard first- and second-order local necessary optimality conditions are sufficient for global optimality when p+1<=n-k.

报告人简介:

夏勇,北京航空航天大学教授,博士生导师,数学科学学院副院长。2002年毕业于北京大学,2007年毕业于中国科学院,师从袁亚湘院士,研究方向为非凸优化,2013年北京青年英才,2018年国家优青,在Math.Program.、SIAM J.Optim.等期刊发表SCI论文70篇。中国运筹学会理事、中国运筹学会数学规划分会常务理事、北京运筹学会理事,中国运筹学会会刊JORSC期刊编委。 代表性工作包括针对经典的二次指派问题提出新模型,被中、美、加、德、意、西班牙等国际国内同行命名为Xia-Yuan线性化,其松弛被称为Xia-Yuan界。

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