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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/2405.01968 |
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| _version_ | 1866917656343347200 |
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| author | Goodwin, Ariel Lewis, Adrian S. Lopez-Acedo, Genaro Nicolae, Adriana |
| author_facet | Goodwin, Ariel Lewis, Adrian S. Lopez-Acedo, Genaro Nicolae, Adriana |
| contents | We consider geodesically convex optimization problems involving distances to a finite set of points $A$ in a CAT(0) cubical complex. Examples include the minimum enclosing ball problem, the weighted mean and median problems, and the feasibility and projection problems for intersecting balls with centers in $A$. We propose a decomposition approach relying on standard Euclidean cutting plane algorithms. The cutting planes are readily derivable from efficient algorithms for computing geodesics in the complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex optimization on CAT(0) cubical complexes Goodwin, Ariel Lewis, Adrian S. Lopez-Acedo, Genaro Nicolae, Adriana Optimization and Control 90C48, 52A41, 57Z25, 65K05 F.2.1 We consider geodesically convex optimization problems involving distances to a finite set of points $A$ in a CAT(0) cubical complex. Examples include the minimum enclosing ball problem, the weighted mean and median problems, and the feasibility and projection problems for intersecting balls with centers in $A$. We propose a decomposition approach relying on standard Euclidean cutting plane algorithms. The cutting planes are readily derivable from efficient algorithms for computing geodesics in the complex. |
| title | Convex optimization on CAT(0) cubical complexes |
| topic | Optimization and Control 90C48, 52A41, 57Z25, 65K05 F.2.1 |
| url | https://arxiv.org/abs/2405.01968 |