报告地点：行健楼-526
邀请人：孙海琳教授
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：杭州电子科技大学理*女王调教-女王调教视频-女王 调教小说教授，博士研究生导师。中国青年科技工作者协会会员、中国运筹学会理事、中国运筹学会数学规划分会青年理事、浙江省数学会理事。研究方向为张量最佳逼近问题的理论与算法及其应用。部分研究成果发表在《Numerische Mathematik》、《SIAM Journal on Matrix Analysis and Applications》、《Communications in Mathematical Sciences》、《Journal of Symbolic Computation》、《Journal of Scientific Computing》、《Physical Review A》等期刊。2017年获得天津市数学会青年研究奖、《Science China-Mathematics》优秀论文奖。已主持完成国家自然科学基金青年项目，正主持国家自然科学基金面上项目一项。
