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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2407.13125 |
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| _version_ | 1866929425987141632 |
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| author | Torres, George D. |
| author_facet | Torres, George D. |
| contents | We provide a local theory for the optimization of the Hausdorff distance between a polytope and a zonotope. To do this, we compute explicit local formulae for the Hausdorff function $d(P, -) : Z_n \to \mathbb{R}$, where $P$ is a fixed polytope and $Z_n$ is the space of rank $n$ zonotopes. This local theory is then used to provide an optimization algorithm based on subgradient descent that converges to critical points of $d(P, -)$. We also express the condition of being at a local minimum as a polyhedral feasibility condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Finding the Closest Zonotope to a Polytope in Hausdorff Distance Torres, George D. Optimization and Control Computational Geometry We provide a local theory for the optimization of the Hausdorff distance between a polytope and a zonotope. To do this, we compute explicit local formulae for the Hausdorff function $d(P, -) : Z_n \to \mathbb{R}$, where $P$ is a fixed polytope and $Z_n$ is the space of rank $n$ zonotopes. This local theory is then used to provide an optimization algorithm based on subgradient descent that converges to critical points of $d(P, -)$. We also express the condition of being at a local minimum as a polyhedral feasibility condition. |
| title | On Finding the Closest Zonotope to a Polytope in Hausdorff Distance |
| topic | Optimization and Control Computational Geometry |
| url | https://arxiv.org/abs/2407.13125 |