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The partially symmetric rank-1 approximation of fourth-order partially symmetric tensors

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Abstract

Finding the partially symmetric rank-1 approximation to a given fourth-order partially symmetric tensor has close relationship with its largest M-eigenvalue. In this paper, we study the partially symmetric rank-1 approximation by a proximal alternating linearized minimization method. Furthermore, the global convergence of the algorithm is established, and several numerical experiments show the efficiency and accuracy of the proposed algorithm.

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Acknowledgements

The authors wish to give their sincere appreciation to the anonymous referees for their valuable suggestions and meaningful comments, which help us to improve the paper significantly.

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Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu, China

    Manman Dong

  2. School of Management Science, Qufu Normal University, Rizhao, 276800, Shandong, China

    Chunyan Wang & Haibin Chen

  3. Department of Basic Teaching, Shandong Water Conservancy Vocational College, Rizhao, 276800, Shandong, China

    Qingni Zhu

Authors
  1. Manman Dong
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  2. Chunyan Wang
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  3. Qingni Zhu
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  4. Haibin Chen
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Correspondence to Haibin Chen.

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This work is supported by the Natural Science Foundation of China (12071249,72072080) and Shandong Provincial Natural Science Foundation of Distinguished Young Scholars (ZR2021JQ01).

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Dong, M., Wang, C., Zhu, Q. et al. The partially symmetric rank-1 approximation of fourth-order partially symmetric tensors. Optim Lett 17, 629–642 (2023). https://doi.org/10.1007/s11590-022-01892-8

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