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The Proximal Gradient Method for Composite Optimization Problems on Riemannian Manifolds

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  • Xiaobo Li

    (School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China)

Abstract

In this paper, the composite optimization problem is studied on Riemannian manifolds. To tackle this problem, the proximal gradient method to solve composite optimization problems is proposed on Riemannian manifolds. Under some reasonable conditions, the convergence of the proximal gradient method with the backtracking procedure in the nonconvex case is presented. Furthermore, a sublinear convergence rate and the complexity result of the proximal gradient method for convex case are also established on Riemannian manifolds.

Suggested Citation

  • Xiaobo Li, 2024. "The Proximal Gradient Method for Composite Optimization Problems on Riemannian Manifolds," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2638-:d:1463664
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    References listed on IDEAS

    as
    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
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