Optimization on Weak Riemannian Manifolds
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910148315840512 |
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| author | Zalbertus, Valentina Pfeffer, Max Schmeding, Alexander |
| author_facet | Zalbertus, Valentina Pfeffer, Max Schmeding, Alexander |
| contents | Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article develops the basic framework for optimization via gradient descent on weak Riemannian manifolds leading to the notion of a Hesse manifold. Further, foundational properties for optimization are established for several classes of weak Riemannian manifolds connected to shape analysis and shape optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimization on Weak Riemannian Manifolds Zalbertus, Valentina Pfeffer, Max Schmeding, Alexander Optimization and Control Differential Geometry 49K27 (primary), 58B20, 58C20, 90C48, 58D30, 49Q10 (secondary) Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article develops the basic framework for optimization via gradient descent on weak Riemannian manifolds leading to the notion of a Hesse manifold. Further, foundational properties for optimization are established for several classes of weak Riemannian manifolds connected to shape analysis and shape optimization. |
| title | Optimization on Weak Riemannian Manifolds |
| topic | Optimization and Control Differential Geometry 49K27 (primary), 58B20, 58C20, 90C48, 58D30, 49Q10 (secondary) |
| url | https://arxiv.org/abs/2603.25396 |