Structural Properties of Faces of the Cone of Copositive Matrices

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...

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Autores principales:	Olga Kostyukova, Tatiana Tchemisova
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	copositive matrices completely positive matrices copositive cone minimal exposed cone Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/52309eb382b94c0cb844a49a51935d60
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spelling	oai:doaj.org-article:52309eb382b94c0cb844a49a51935d602021-11-11T18:15:42ZStructural Properties of Faces of the Cone of Copositive Matrices10.3390/math92126982227-7390https://doaj.org/article/52309eb382b94c0cb844a49a51935d602021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2698https://doaj.org/toc/2227-7390In 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.Olga KostyukovaTatiana TchemisovaMDPI AGarticlecopositive matricescompletely positive matricescopositive coneminimal exposed coneMathematicsQA1-939ENMathematics, Vol 9, Iss 2698, p 2698 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	copositive matrices completely positive matrices copositive cone minimal exposed cone Mathematics QA1-939
spellingShingle	copositive matrices completely positive matrices copositive cone minimal exposed cone Mathematics QA1-939 Olga Kostyukova Tatiana Tchemisova Structural Properties of Faces of the Cone of Copositive Matrices
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.
format	article
author	Olga Kostyukova Tatiana Tchemisova
author_facet	Olga Kostyukova Tatiana Tchemisova
author_sort	Olga Kostyukova
title	Structural Properties of Faces of the Cone of Copositive Matrices
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
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/52309eb382b94c0cb844a49a51935d60
work_keys_str_mv	AT olgakostyukova structuralpropertiesoffacesoftheconeofcopositivematrices AT tatianatchemisova structuralpropertiesoffacesoftheconeofcopositivematrices
_version_	1718431883561271296

Structural Properties of Faces of the Cone of Copositive Matrices

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