Structural properties of faces of the cone of copositive matrices

Detalhes bibliográficos
Autor(a) principal: Kostyukova, Olga
Data de Publicação: 2021
Outros Autores: Tchemisova, Tatiana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/32544
Resumo: In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.
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spelling Structural properties of faces of the cone of copositive matricesCopositive matricesCompletely positive matricesCopositive coneMinimal exposed coneIn this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.MDPI2021-11-03T16:39:41Z2021-11-01T00:00:00Z2021-11-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/32544eng10.3390/math9212698Kostyukova, OlgaTchemisova, Tatianainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:02:37Zoai:ria.ua.pt:10773/32544Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:04:08.801661Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Structural properties of faces of the cone of copositive matrices
title Structural properties of faces of the cone of copositive matrices
spellingShingle Structural properties of faces of the cone of copositive matrices
Kostyukova, Olga
Copositive matrices
Completely positive matrices
Copositive cone
Minimal exposed cone
title_short Structural properties of faces of the cone of copositive matrices
title_full Structural properties of faces of the cone of copositive matrices
title_fullStr Structural properties of faces of the cone of copositive matrices
title_full_unstemmed Structural properties of faces of the cone of copositive matrices
title_sort Structural properties of faces of the cone of copositive matrices
author Kostyukova, Olga
author_facet Kostyukova, Olga
Tchemisova, Tatiana
author_role author
author2 Tchemisova, Tatiana
author2_role author
dc.contributor.author.fl_str_mv Kostyukova, Olga
Tchemisova, Tatiana
dc.subject.por.fl_str_mv Copositive matrices
Completely positive matrices
Copositive cone
Minimal exposed cone
topic Copositive matrices
Completely positive matrices
Copositive cone
Minimal exposed cone
description In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.
publishDate 2021
dc.date.none.fl_str_mv 2021-11-03T16:39:41Z
2021-11-01T00:00:00Z
2021-11-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/32544
url http://hdl.handle.net/10773/32544
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/math9212698
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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