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Cholesky QR-based retraction on the generalized Stiefel manifold

Author

Listed:
  • Hiroyuki Sato

    (Kyoto University
    Kyoto University)

  • Kensuke Aihara

    (Tokyo City University)

Abstract

When optimizing on a Riemannian manifold, it is important to use an efficient retraction, which maps a point on a tangent space to a point on the manifold. In this paper, we prove a map based on the QR factorization to be a retraction on the generalized Stiefel manifold. In addition, we propose an efficient implementation of the retraction based on the Cholesky QR factorization. Numerical experiments show that the proposed retraction is more efficient than the existing one based on the polar factorization.

Suggested Citation

  • Hiroyuki Sato & Kensuke Aihara, 2019. "Cholesky QR-based retraction on the generalized Stiefel manifold," Computational Optimization and Applications, Springer, vol. 72(2), pages 293-308, March.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0046-7
    DOI: 10.1007/s10589-018-0046-7
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    References listed on IDEAS

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    1. Hiroyuki Sato, 2016. "A Dai–Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions," Computational Optimization and Applications, Springer, vol. 64(1), pages 101-118, May.
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    Cited by:

    1. Yuya Yamakawa & Hiroyuki Sato, 2022. "Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method," Computational Optimization and Applications, Springer, vol. 81(2), pages 397-421, March.
    2. Ke Wang & Zhuo Chen & Shihui Ying & Xinjian Xu, 2023. "Low-Rank Matrix Completion via QR-Based Retraction on Manifolds," Mathematics, MDPI, vol. 11(5), pages 1-17, February.

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