The Riemannian Convex Bundle Method
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912489740959744 |
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| author | Bergmann, Ronny Herzog, Roland Jasa, Hajg |
| author_facet | Bergmann, Ronny Herzog, Roland Jasa, Hajg |
| contents | We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallelly transported into the current serious iterate. This approach generalizes the dual form of classical bundle subproblems in Euclidean space. We prove that, under mild conditions, the convex bundle method converges to a minimizer. Several numerical examples implemented using Manopt$.$jl illustrate the performance of the proposed method and compare it to the subgradient method, the cyclic proximal point algorithm, as well as the proximal bundle method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Riemannian Convex Bundle Method Bergmann, Ronny Herzog, Roland Jasa, Hajg Optimization and Control Numerical Analysis Differential Geometry We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallelly transported into the current serious iterate. This approach generalizes the dual form of classical bundle subproblems in Euclidean space. We prove that, under mild conditions, the convex bundle method converges to a minimizer. Several numerical examples implemented using Manopt$.$jl illustrate the performance of the proposed method and compare it to the subgradient method, the cyclic proximal point algorithm, as well as the proximal bundle method. |
| title | The Riemannian Convex Bundle Method |
| topic | Optimization and Control Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2402.13670 |