学术报告

【online】Sphere covering and approximating tensor norms

发布人:发布时间: 2021-08-24

字体大小: 【小】 【中】 【大】

题目:Sphere covering and approximating tensor norms

 

告人:江波 (上海财经大学教授)

 

摘要:It is known that computing the spectral norm and the nuclear norm of a tensor is NP-hard in general. In this talk, we focus on approximating tensor spectral norm and the nuclear norm, and relate those problems to the sphere covering problem. We provide several constructive methods to cover the n dimensional sphere by a limited number of sphere caps. Those methods demonstrate the tradeoff between the number of caps required to cover the whole sphere and the radius of each cap. One of the method leads to an universal approximating algorithm of computing tensor spectral norm with (ln(n)/n)^{1/2} approximation ratio, and consequently yields a (ln(n)/n)^{1/2} approximating algorithm of computing tensor nuclear norm, which improves upon the previous approximating algorithm with (1/n)^{1/2} ratio.

 

时间:2021年827日上午1000

 

报告方式: 腾讯会议 ID: 323 226 684 会议密码:123456

 

江波,上海财经大学信息管理与工程学院、交叉科学研究院常聘教授。他于20139月在美国明尼苏达大学获得博士学位。主要研究优化理论及其在收益管理、机器学习等领域中的应用。在运筹优化领域的国际著名杂志Operations ResearchMathematics of Operations ResearchMathematical ProgrammingSIAM Journal on Optimization等发表过多篇论文。主持过多项国家自然科学基金;获得过中国运筹学会青年科技奖、上海市高校特聘教授(东方学者)、上海市拔尖人才、上海市自然科学奖二等奖等荣誉。

 

 

邀请人:陶敏  老师