A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors
In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same express...
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| Vydáno v: | Applied numerical mathematics Ročník 182; s. 235 - 247 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.12.2022
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| ISSN: | 0168-9274, 1873-5460 |
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| Abstract | In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same expression as the Polar decomposition. We establish that the global convergence of our algorithm. Preliminary results show that the computational advantage of our algorithm. |
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| AbstractList | In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same expression as the Polar decomposition. We establish that the global convergence of our algorithm. Preliminary results show that the computational advantage of our algorithm. |
| Author | Sheng, Zhou Yang, Weiwei Wen, Jie |
| Author_xml | – sequence: 1 givenname: Zhou surname: Sheng fullname: Sheng, Zhou email: szhou03@live.com, shengz@ahut.edu.cn organization: School of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243032, China – sequence: 2 givenname: Weiwei surname: Yang fullname: Yang, Weiwei email: yangweiwei0810@126.com organization: School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, Jiangsu 211816, China – sequence: 3 givenname: Jie surname: Wen fullname: Wen, Jie email: wenjie@nuaa.edu.cn organization: College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, China |
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| Cites_doi | 10.1007/s11075-008-9251-2 10.1137/110835335 10.1137/100801482 10.1109/MSP.2013.2297439 10.1137/S0895479896305696 10.1137/S0895479801387413 10.1137/07070111X 10.1016/0165-1684(94)90029-9 10.1137/100802529 10.1007/s10589-019-00128-3 10.1137/040605266 10.1002/nla.2180 10.1137/11085743X 10.1137/19M125950X 10.1093/imanum/8.1.141 10.1137/070711621 10.1137/090764827 10.1137/S0895479899352045 10.1007/s10589-015-9801-1 10.1137/090763172 10.1137/17M1116295 10.1080/02331934.2013.836650 10.1137/S0895479898346995 10.1007/s10915-013-9740-x 10.1016/j.laa.2011.12.007 10.1137/140957822 10.1016/j.laa.2011.10.033 10.1016/j.laa.2016.10.019 10.1137/S0895479800368354 10.1137/060655924 10.1137/16M1098759 10.1007/s10107-012-0584-1 10.1137/130935112 |
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| Keywords | Riemannian gradient Global convergence Tensor approximation Łojasiewicz gradient inequality Symmetric tensor |
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| SubjectTerms | Global convergence Riemannian gradient Symmetric tensor Tensor approximation Łojasiewicz gradient inequality |
| Title | A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors |
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