Optimization hierarchies for distance-avoiding sets in compact spaces
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866916951168647168 |
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| author | Bekker, Bram Kuryatnikova, Olga Filho, Fernando Mário de Oliveira Vera, Juan C. |
| author_facet | Bekker, Bram Kuryatnikova, Olga Filho, Fernando Mário de Oliveira Vera, Juan C. |
| contents | Witsenhausen's problem asks for the maximum fraction $α_n$ of the $n$-dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. The best upper bounds for $α_n$ are given by extensions of the Lovász theta number. In this paper, optimization hierarchies based on the Lovász theta number, like the Lasserre hierarchy, are extended to Witsenhausen's problem and similar problems. These hierarchies are shown to converge and are used to compute the best upper bounds for $α_n$ in low dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05429 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimization hierarchies for distance-avoiding sets in compact spaces Bekker, Bram Kuryatnikova, Olga Filho, Fernando Mário de Oliveira Vera, Juan C. Metric Geometry Optimization and Control 46N10, 52C10, 51K99, 90C22, 90C34 Witsenhausen's problem asks for the maximum fraction $α_n$ of the $n$-dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. The best upper bounds for $α_n$ are given by extensions of the Lovász theta number. In this paper, optimization hierarchies based on the Lovász theta number, like the Lasserre hierarchy, are extended to Witsenhausen's problem and similar problems. These hierarchies are shown to converge and are used to compute the best upper bounds for $α_n$ in low dimensions. |
| title | Optimization hierarchies for distance-avoiding sets in compact spaces |
| topic | Metric Geometry Optimization and Control 46N10, 52C10, 51K99, 90C22, 90C34 |
| url | https://arxiv.org/abs/2304.05429 |