学术报告

报告题目: Sphere covering and approximating tensor norms

报告人：江波（上海财经大学教授，博士生导师）

报告时间：2021年7月15日下午15：00—17：00

报告地点：25教14楼学术报告厅

主办单位:数学与统计学院

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.

报告人简介：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，博士生导师，副院长。他于2013年9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 Research、Mathematics of Operations Research、Mathematical Programming、SIAM 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。

欢迎大家光临！