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(xué) 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(xué)理學(xué)院教授，博士研究生導(dǎo)師。研究方向為張量優(yōu)化計算的理論與算法及其應(yīng)用。先后在新加坡國立大學(xué)數(shù)學(xué)系和芝加哥大學(xué)統(tǒng)計系從事博士后研究工作。多次在北京大學(xué)數(shù)學(xué)學(xué)院、韓國國家數(shù)學(xué)研究所、加州大學(xué)伯克利分校、香港理工大學(xué)、新南威爾士大學(xué)進行學(xué)術(shù)訪問。中國運籌學(xué)會數(shù)學(xué)優(yōu)化分會青年理事，美國數(shù)學(xué)會Math Review 評論員。 共計發(fā)表SCI 論文40 余篇，部分研究成果發(fā)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(yōu)秀論文獎等。
 理學(xué)院
2019年9月7日