Complete positivity and distance-avoiding sets

We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to rep...

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Detalles Bibliográficos
Autores principales: DeCorte, Evan, Filho, Fernando Mário de Oliveira, Vallentin, Frank
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Full Length Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8863813/
https://www.ncbi.nlm.nih.gov/pubmed/35250093
http://dx.doi.org/10.1007/s10107-020-01562-6
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author DeCorte, Evan
Filho, Fernando Mário de Oliveira
Vallentin, Frank
author_facet DeCorte, Evan
Filho, Fernando Mário de Oliveira
Vallentin, Frank
author_sort DeCorte, Evan
collection PubMed
description We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space.
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spelling pubmed-88638132022-03-02 Complete positivity and distance-avoiding sets DeCorte, Evan Filho, Fernando Mário de Oliveira Vallentin, Frank Math Program Full Length Paper We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space. Springer Berlin Heidelberg 2020-09-16 2022 /pmc/articles/PMC8863813/ /pubmed/35250093 http://dx.doi.org/10.1007/s10107-020-01562-6 Text en © The Author(s) 2020 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Full Length Paper
DeCorte, Evan
Filho, Fernando Mário de Oliveira
Vallentin, Frank
Complete positivity and distance-avoiding sets
title Complete positivity and distance-avoiding sets
title_full Complete positivity and distance-avoiding sets
title_fullStr Complete positivity and distance-avoiding sets
title_full_unstemmed Complete positivity and distance-avoiding sets
title_short Complete positivity and distance-avoiding sets
title_sort complete positivity and distance-avoiding sets
topic Full Length Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8863813/
https://www.ncbi.nlm.nih.gov/pubmed/35250093
http://dx.doi.org/10.1007/s10107-020-01562-6
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