Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations

doi:10.1007/s10107-022-01867-8

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	Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations
	Hu, Shenglong 1; Ye, Ke 2
	2022-07-30
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
页码	60
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 paper, 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.
关键词	Orthogonally decomposable tensors Low rank orthogonal tensor approximation R-linear convergence Sublinear convergence Global convergence
DOI	10.1007/s10107-022-01867-8
收录类别	SCI
语种	英语
资助项目	National Science Foundation of China[11801548] ; National Science Foundation of China[11688101] ; Young Elite Scientists Sponsorship Program by Tianjin ; Natural Science Foundation of Zhejiang Province, China[LD19A010002] ; Natural Science Foundation of Zhejiang Province, China[LY22A010022] ; National Key R&D Program of China[2018YFA0306702] ; National Key R&D Program of China[2020YFA0712300] ; CAS Project for Young Scientists in Basic Research[YSBR-008]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000833457000001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61170
专题	中国科学院数学与系统科学研究院
通讯作者	Ye, Ke
作者单位	1.Hangzhou Dianzi Univ, Sch Sci, Dept Math, Hangzhou 310018, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu, Shenglong,Ye, Ke. Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations[J]. MATHEMATICAL PROGRAMMING,2022:60.
APA	Hu, Shenglong,&Ye, Ke.(2022).Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations.MATHEMATICAL PROGRAMMING,60.
MLA	Hu, Shenglong,et al."Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations".MATHEMATICAL PROGRAMMING (2022):60.