优化系列报告2
题目：Linear Convergence of an Alternating Polar Decomposition Method for Low Rank Orthogonal Tensor Approximations
报告人：胡胜龙教授（杭州电子科技大学）
时间：2020年11月18日16：00-18：00
腾讯会议ID： 930 456 865
摘要： Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating polar decomposition method (APD). In this talk, an improved version iAPD of the classical APD is proposed. For the first time, all of the following four fundamental properties are established for iAPD: (i) the algorithm converges globally and the whole sequence converges to a KKT point without any assumption; (ii) it exhibits an overall sublinear convergence with an explicit rate which is sharper than the usual $O(1/k)$ for first order methods in optimization; (iii) more importantly, it converges $R$-linearly for a generic tensor without any assumption; (iv) for almost all LROTA problems, iAPD reduces to APD after finitely many iterations if it converges to a local minimizer.
个人简介：胡胜龙，杭州电子科技大学理学院教授，博士研究生导师。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
