An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

doi:10.1007/s40305-022-00422-8

Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (2): 461-477.doi: 10.1007/s40305-022-00422-8

收稿日期:2021-03-09 修回日期:2022-03-10 出版日期:2024-06-30 发布日期:2024-06-12
通讯作者: Xi-Hong Yan, Chuan-Long Wang, Xiong-Wei Guo E-mail:xihong1@e.ntu.edu.sg;clwang1964@163.com;gxw_0427@163.com

An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

Chuan-Long Wang^1,2, Xiong-Wei Guo^1,2, Xi-Hong Yan²

1 Key Laboratory of Engineering and Computational Science, Shanxi Provincial Department of Education, Jinzhong 030619, Shanxi, China;
2 Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, Shanxi, China

Received:2021-03-09 Revised:2022-03-10 Online:2024-06-30 Published:2024-06-12
Contact: Xi-Hong Yan, Chuan-Long Wang, Xiong-Wei Guo E-mail:xihong1@e.ntu.edu.sg;clwang1964@163.com;gxw_0427@163.com

摘要/Abstract

Abstract: In this paper, an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems. In our method, the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set. Moreover, due to the special properties of Hankel structure, using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost. Meanwhile, the convergence of the new algorithm is discussed under some reasonable conditions. Finally, the numerical experiments show the effectiveness of the proposed algorithm.

Key words: Hankel tensor, Tensor completion, Accelerated proximal gradient algorithm

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2024, 12(2): 461-477.

Chuan-Long Wang, Xiong-Wei Guo, Xi-Hong Yan. An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion[J]. Journal of the Operations Research Society of China, 2024, 12(2): 461-477.

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An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

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