Approximate cone factorizations and lifts of polytopes
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/44072 https://doi.org/10.1007/s10107-014-0848-z |
Resumo: | In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficient representations using second order cones. We establish a direct relationship between the quality of the factorization and the quality of the approximations, and our results extend to generalized slack matrices that arise from a polytope contained in a polyhedron. |
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Approximate cone factorizations and lifts of polytopesIn this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficient representations using second order cones. We establish a direct relationship between the quality of the factorization and the quality of the approximations, and our results extend to generalized slack matrices that arise from a polytope contained in a polyhedron.Springer2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44072http://hdl.handle.net/10316/44072https://doi.org/10.1007/s10107-014-0848-zhttps://doi.org/10.1007/s10107-014-0848-zenghttps://doi.org/10.1007/s10107-014-0848-zGouveia, JoãoParrilo, Pablo A.Thomas, Rekha R.info: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:RCAAP2021-06-29T10:02:52Zoai:estudogeral.uc.pt:10316/44072Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:31.396605Repositório 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 |
Approximate cone factorizations and lifts of polytopes |
title |
Approximate cone factorizations and lifts of polytopes |
spellingShingle |
Approximate cone factorizations and lifts of polytopes Gouveia, João |
title_short |
Approximate cone factorizations and lifts of polytopes |
title_full |
Approximate cone factorizations and lifts of polytopes |
title_fullStr |
Approximate cone factorizations and lifts of polytopes |
title_full_unstemmed |
Approximate cone factorizations and lifts of polytopes |
title_sort |
Approximate cone factorizations and lifts of polytopes |
author |
Gouveia, João |
author_facet |
Gouveia, João Parrilo, Pablo A. Thomas, Rekha R. |
author_role |
author |
author2 |
Parrilo, Pablo A. Thomas, Rekha R. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Gouveia, João Parrilo, Pablo A. Thomas, Rekha R. |
description |
In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficient representations using second order cones. We establish a direct relationship between the quality of the factorization and the quality of the approximations, and our results extend to generalized slack matrices that arise from a polytope contained in a polyhedron. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/44072 http://hdl.handle.net/10316/44072 https://doi.org/10.1007/s10107-014-0848-z https://doi.org/10.1007/s10107-014-0848-z |
url |
http://hdl.handle.net/10316/44072 https://doi.org/10.1007/s10107-014-0848-z |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1007/s10107-014-0848-z |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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 |
repository.mail.fl_str_mv |
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1799133821650599936 |