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Rank-one approximation of a higher-order tensor by a Riemannian trust-region method

Author

Listed:
  • Jianheng Chen

    (Zhejiang University of Water Resources and Electric Power
    Xiamen University)

  • Wen Huang

    (Xiamen University)

Abstract

In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on tangent vectors to the Cartesian product of manifolds. A Riemannian trust-region method with block-diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in the literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective.

Suggested Citation

  • Jianheng Chen & Wen Huang, 2025. "Rank-one approximation of a higher-order tensor by a Riemannian trust-region method," Computational Optimization and Applications, Springer, vol. 90(2), pages 515-556, March.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:2:d:10.1007_s10589-024-00634-z
    DOI: 10.1007/s10589-024-00634-z
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    References listed on IDEAS

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    1. Alhussein Fawzi & Matej Balog & Aja Huang & Thomas Hubert & Bernardino Romera-Paredes & Mohammadamin Barekatain & Alexander Novikov & Francisco J. R. Ruiz & Julian Schrittwieser & Grzegorz Swirszcz & , 2022. "Discovering faster matrix multiplication algorithms with reinforcement learning," Nature, Nature, vol. 610(7930), pages 47-53, October.
    2. Yuning Yang & Qingzhi Yang & Liqun Qi, 2014. "Properties and methods for finding the best rank-one approximation to higher-order tensors," Computational Optimization and Applications, Springer, vol. 58(1), pages 105-132, May.
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