Best Nonnegative Rank-One Approximations of Tensors

来源: 理学院 作者:马国强 添加日期:2019-09-08 16:10:07 阅读次数:
报告题目: Best Nonnegative Rank-One Approximations of Tensors
报告人:胡胜龙(杭州电子科技大学 教授)
报告时间:2019年9月10日 15:00
报告摘要:In this talk, we discuss the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-hard in general, and includes the problem of finding the best nonnegative rank-one approximation of a given tensor. A Positivstellensatz is given for this class of polynomial optimization problems, based on which a globally convergent hierarchy of doubly nonnegative (DNN) relaxations is proposed. A (zero-th order) DNN relaxation method is applied to solve these problems, resulting in linear matrix optimization problems under both the positive semidefinite and nonnegative conic constraints. A worst case approximation bound is given for this relaxation method. Then, the recent solver SDPNAL+ is adopted to solve this class of matrix optimization problems. Typically, the DNN relaxations are tight, and hence the best nonnegative rank-one approximation of a tensor can be revealed frequently.Numerical experiments is reported as well.
报告人简介:胡胜龙,杭州电子科技大学理学院教授,博士研究生导师。研究方向为张量优化计算的理论与算法及其应用。先后在新加坡国立大学数学系和芝加哥大学统计系从事博士后研究工作。多次在北京大学数学学院、韩国国家数学研究所、加州大学伯克利分校、香港理工大学、新南威尔士大学进行学术访问。中国运筹学会数学优化分会青年理事,美国数学会Math Review 评论员。 共计发表SCI 论文40 余篇,部分研究成果发表在国际顶级期刊Numerische Mathematik、SIAM Journal on Matrix Analysis and Applications、Communications in Mathematical Sciences、Journal of Symbolic Computation、Journal of Scientific Computing、Physical Review A 等。 5 篇论文被列入ESI 高被引用榜,Web of Science 他引超过520 次。曾获SIAM Early Career Travel Award、Science China-Mathematics 优秀论文奖等。