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Proximal gradient algorithm with trust region scheme on Riemannian manifold

Author

Listed:
  • Shimin Zhao

    (Nanjing University of Science and Technology)

  • Tao Yan

    (Nanjing University of Science and Technology)

  • Yuanguo Zhu

    (Nanjing University of Science and Technology)

Abstract

We consider the problem of minimizing the sum of a smooth function and nonsmooth function over a Riemannian manifold. We develop a Riemannian proximal gradient algorithm with a trust region scheme for the problem. Global convergence is presented under natural assumptions. We establish an $$O(1/{\varepsilon ^2})$$ O ( 1 / ε 2 ) iteration complexity bound that matches the best-known complexity bound of Riemannian trust region methods for smooth optimization. Moreover, we give a nonmonotone version and an accelerated version of the Riemannian proximal gradient algorithm with a trust region scheme. Their global convergence is established. Numerical results demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Shimin Zhao & Tao Yan & Yuanguo Zhu, 2024. "Proximal gradient algorithm with trust region scheme on Riemannian manifold," Journal of Global Optimization, Springer, vol. 88(4), pages 1051-1076, April.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:4:d:10.1007_s10898-023-01326-4
    DOI: 10.1007/s10898-023-01326-4
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    References listed on IDEAS

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    1. Jianjun Liu & Xiangmin Xu & Xuehui Cui, 2018. "An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 69(1), pages 77-97, January.
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