Riemannian Gradient Method with Momentum
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918369694842880 |
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| author | Leggio, Filippo Scuppa, Diego |
| author_facet | Leggio, Filippo Scuppa, Diego |
| contents | In this paper, we consider the problem of minimizing a smooth function on a Riemannian manifold and present a Riemannian gradient method with momentum. The proposed algorithm represents a substantial and nontrivial extension of a recently introduced method for unconstrained optimization. We prove that the algorithm, supported by a safeguarding rule, produces an $ε$-stationary point with a worst-case complexity bound of $\mathcal{O}(ε^{-2})$. Extensive computational experiments on benchmark problems are carried out, comparing the proposed method with state-of-the-art solvers available in the Manopt package. The results demonstrate competitive and often superior performance. Overall, the numerical evidence confirms the effectiveness and robustness of the proposed approach, which provides a meaningful extension of the recently introduced momentum-based method to Riemannian optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04078 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Riemannian Gradient Method with Momentum Leggio, Filippo Scuppa, Diego Optimization and Control 90C26, 90C30, 90C53, 90C60 In this paper, we consider the problem of minimizing a smooth function on a Riemannian manifold and present a Riemannian gradient method with momentum. The proposed algorithm represents a substantial and nontrivial extension of a recently introduced method for unconstrained optimization. We prove that the algorithm, supported by a safeguarding rule, produces an $ε$-stationary point with a worst-case complexity bound of $\mathcal{O}(ε^{-2})$. Extensive computational experiments on benchmark problems are carried out, comparing the proposed method with state-of-the-art solvers available in the Manopt package. The results demonstrate competitive and often superior performance. Overall, the numerical evidence confirms the effectiveness and robustness of the proposed approach, which provides a meaningful extension of the recently introduced momentum-based method to Riemannian optimization. |
| title | Riemannian Gradient Method with Momentum |
| topic | Optimization and Control 90C26, 90C30, 90C53, 90C60 |
| url | https://arxiv.org/abs/2603.04078 |