数学与统计学院学术报告[2021] 116号

(高水平大学建设系列报告516号)

报告题目: Convergence analysis for low rank partially orthogonal tensor approximation problem

报告人：叶科　 副研究员  （中国科学院数学与系统科学研究院）

报告时间：2021年11月24日 　14:50-15:40

直播平台及链接： 腾讯会议 会议ID：647 171 244  

报告内容：Low rank partially orthogonal tensor approximation (LRPOTA) is an important problem in tensor computations and their applications. It includes Low rank orthogonal tensor approximation (LROTA) problem as a special case. A classical and widely used algorithm for the LRPOTA problem is the alternating least square and polar decomposition method (ALS-APD). In this talk, we will introduce an improved version ALS-iAPD of the classical ALS-APD, for which all the following three fundamental properties will be addressed: (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. I will explain how algebraic and differential geometric tools are used to obtain these results in optimization theory. This talk is based on joint works with Shenglong Hu.  

报告人简历：

叶科，中国科学院数学与系统科学研究院副研究员，入选海外高层次人才引进计划（青年项目）,中科院百人计划（C类），中科院基础研究领域青年团队计划，以及中科院“陈景润未来之星”。研究兴趣是代数几何及微分几何在计算复杂度理论，（多重）线性代数，数值计算以及优化问题中的应用。工作主要发表于Adv. Math., FoCM, Math. Program., SIMAX, IEEE Info. Theory等重要国际期刊。

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                                                2021年11月22日