Optimization hierarchies for distance-avoiding sets in compact spaces

Bram Bekker; Olga Kuryatnikova; Juan Carlos Vera Lizcano; Fernando De Oliveira Filho

Optimization hierarchies for distance-avoiding sets in compact spaces

Bram Bekker, Olga Kuryatnikova^*, Juan Carlos Vera Lizcano, Fernando De Oliveira Filho

^*Corresponding author for this work

Econometrics

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Abstract

Witsenhausen’s problem asks for the maximum fraction αn 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 αn are given by extensions of the Lov´asz theta number. In this paper, optimization hierarchies based on the Lov´asz 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 αn in low dimensions.

Original language	English
Number of pages	34
Journal	arXiv preprint
Publication status	Published - 2023

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Optimization hierarchies for distance-avoiding sets in compact spacesFinal published version, 441 KBLicence: Article 25fa Dutch Copyright Act

https://arxiv.org/pdf/2304.05429Licence: Unspecified

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@article{2c01d42625c9468c9bad544e3a3418d3,

title = "Optimization hierarchies for distance-avoiding sets in compact spaces",

abstract = "Witsenhausen{\textquoteright}s problem asks for the maximum fraction αn 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 αn are given by extensions of the Lov´asz theta number. In this paper, optimization hierarchies based on the Lov´asz theta number, like the Lasserre hierarchy, are extended to Witsenhausen{\textquoteright}s problem and similar problems. These hierarchies are shown to converge and are used to compute the best upper bounds for αn in low dimensions.",

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T1 - Optimization hierarchies for distance-avoiding sets in compact spaces

AU - Bekker, Bram

AU - Kuryatnikova, Olga

AU - Lizcano, Juan Carlos Vera

AU - De Oliveira Filho, Fernando

PY - 2023

Y1 - 2023

N2 - Witsenhausen’s problem asks for the maximum fraction αn 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 αn are given by extensions of the Lov´asz theta number. In this paper, optimization hierarchies based on the Lov´asz 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 αn in low dimensions.

AB - Witsenhausen’s problem asks for the maximum fraction αn 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 αn are given by extensions of the Lov´asz theta number. In this paper, optimization hierarchies based on the Lov´asz 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 αn in low dimensions.

M3 - Article

JO - arXiv preprint

JF - arXiv preprint

ER -

Optimization hierarchies for distance-avoiding sets in compact spaces

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