報告題目： Best Nonnegative Rank-One Approximations of Tensors
報告人：胡勝龍（杭州電子科技大學 教授）
報告時間：2019年9月10日 15:00
報告地點：格致中樓500會議室
報告摘要：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.
報告人簡介：胡勝龍，杭州電子科技大學理學院教授，博士研究生導師。研究方向為張量優化計算的理論與算法及其應用。先后在新加坡國立大學數學系和芝加哥大學統計系從事博士后研究工作。多次在北京大學數學學院、韓國國家數學研究所、加州大學伯克利分校、香港理工大學、新南威爾士大學進行學術訪問。中國運籌學會數學優化分會青年理事，美國數學會Math Review 評論員。 共計發表SCI 論文40 余篇，部分研究成果發表在國際頂級期刊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 篇論文被列入ESI 高被引用榜，Web of Science 他引超過520 次。曾獲SIAM Early Career Travel Award、Science China-Mathematics 優秀論文獎等。
 理學院
2019年9月7日