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.
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Chuan-long Wang: Conceptualization, Methodology, Supervision; Xiong-wei Guo: Software, Writing - Original Draft, Writing - Review & Editing; Xi-hong Yan: Funding acquisition, Project administration, Supervision.
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Wang, CL., Guo, XW. & Yan, XH. An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion. J. Oper. Res. Soc. China 12, 461–477 (2024). https://doi.org/10.1007/s40305-022-00422-8
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DOI: https://doi.org/10.1007/s40305-022-00422-8