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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13316 |
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| _version_ | 1866910306609922048 |
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| author | Zhou, Li-wen Liu, Ling-ling Min, Chao Zhang, Yao-jia Huang, Nan-Jing |
| author_facet | Zhou, Li-wen Liu, Ling-ling Min, Chao Zhang, Yao-jia Huang, Nan-Jing |
| contents | In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set on a Riemannian manifold. As applications, some optimality conditions are obtained for optimization problems with constraints on Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds Zhou, Li-wen Liu, Ling-ling Min, Chao Zhang, Yao-jia Huang, Nan-Jing Optimization and Control In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set on a Riemannian manifold. As applications, some optimality conditions are obtained for optimization problems with constraints on Riemannian manifolds. |
| title | On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.13316 |