Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/114554
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Gouveia, João | - |
dc.contributor.author | Lourenço, Bruno F. | - |
dc.date.accessioned | 2024-04-01T09:53:08Z | - |
dc.date.available | 2024-04-01T09:53:08Z | - |
dc.date.issued | 2022-07-24 | - |
dc.identifier.issn | 0895-4798 | pt |
dc.identifier.issn | 1095-7162 | pt |
dc.identifier.uri | https://hdl.handle.net/10316/114554 | - |
dc.description | 27 pages, 4 figures. Some minor fixes. To appear at the SIAM Journal on Matrix Analysis | pt |
dc.description.abstract | We analyze self-dual polyhedral cones and prove several properties about their slack matrices. In particular, we show that self-duality is equivalent to the existence of a positive semidefinite (PSD) slack. Beyond that, we show that if the underlying cone is irreducible, then the corresponding PSD slacks are not only doubly nonnegative matrices (DNN) but are extreme rays of the cone of DNN matrices, which correspond to a family of extreme rays not previously described. More surprisingly, we show that, unless the cone is simplicial, PSD slacks not only fail to be completely positive matrices but they also lie outside the cone of completely positive semidefinite matrices. Finally, we show how one can use semidefinite programming to probe the existence of self-dual cones with given combinatorics. Our results are given for polyhedral cones but we also discuss some consequences for negatively self-polar polytopes. | pt |
dc.description.sponsorship | JSPS Grant-in-Aid for Early-Career Scientists grant JP19K20217 and the Grant-in-Aid for Scientific Research (B) grant JP21H03398. | pt |
dc.language.iso | eng | pt |
dc.publisher | Society for Industrial and Applied Mathematics | pt |
dc.relation | info:eu-repo/grantAgreement/UIDB/00324/2020 | pt |
dc.rights | openAccess | pt |
dc.subject | self-dual cone | pt |
dc.subject | slack matrix | pt |
dc.subject | polyhedral cone | pt |
dc.subject | polytope | pt |
dc.subject | doubly nonnegative matrix | pt |
dc.subject | completely positive semidefinite matrix | pt |
dc.subject | completely positive matrix | pt |
dc.title | Self-dual polyhedral cones and their slack matrices | pt |
dc.type | article | - |
degois.publication.firstPage | 1096 | pt |
degois.publication.lastPage | 1121 | pt |
degois.publication.issue | 3 | pt |
degois.publication.title | SIAM Journal on Matrix Analysis and Applications | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.1137/22M1519869 | pt |
degois.publication.volume | 44 | pt |
dc.date.embargo | 2022-07-24 | * |
uc.date.periodoEmbargo | 0 | pt |
item.fulltext | Com Texto completo | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.languageiso639-1 | en | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.grantfulltext | open | - |
crisitem.project.grantno | Center for Mathematics, University of Coimbra- CMUC | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-8345-9754 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
SELF-DUAL POLYHEDRAL CONES AND THEIR SLACK MATRICES.pdf | 677.45 kB | Adobe PDF | View/Open |
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