Euclidean distance degree in manifold optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909493622734848 |
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| author | Lai, Zehua Lim, Lek-Heng Ye, Ke |
| author_facet | Lai, Zehua Lim, Lek-Heng Ye, Ke |
| contents | We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we will also determine the Euclidean distance degree of an important class of Schubert varieties that often appear in applications. Our technique goes further than furnishing the value of the Euclidean distance degree; it will also yield closed-form expressions for all stationary points of the Euclidean distance function in each instance. We will discuss the implications of these results on the tractability of manifold optimization problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euclidean distance degree in manifold optimization Lai, Zehua Lim, Lek-Heng Ye, Ke Optimization and Control Algebraic Geometry Differential Geometry 14M15, 15A24, 58C05, 58K05, 90C26 We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we will also determine the Euclidean distance degree of an important class of Schubert varieties that often appear in applications. Our technique goes further than furnishing the value of the Euclidean distance degree; it will also yield closed-form expressions for all stationary points of the Euclidean distance function in each instance. We will discuss the implications of these results on the tractability of manifold optimization problems. |
| title | Euclidean distance degree in manifold optimization |
| topic | Optimization and Control Algebraic Geometry Differential Geometry 14M15, 15A24, 58C05, 58K05, 90C26 |
| url | https://arxiv.org/abs/2502.10336 |