Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations
文献类型：期刊论文
| 作者 | Hu, Shenglong1; Ye, Ke2 |
| 刊名 | MATHEMATICAL PROGRAMMING
 |
| 出版日期 | 2022-07-30 |
| 页码 | 60 |
| 关键词 | Orthogonally decomposable tensors Low rank orthogonal tensor approximation R-linear convergence Sublinear convergence Global convergence |
| ISSN号 | 0025-5610 |
| DOI | 10.1007/s10107-022-01867-8 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000833457000001 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61169]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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