Utilize este identificador para referenciar este registo: https://hdl.handle.net/10316/114554
Título: Self-dual polyhedral cones and their slack matrices
Autor: Gouveia, João 
Lourenço, Bruno F.
Palavras-chave: self-dual cone; slack matrix; polyhedral cone; polytope; doubly nonnegative matrix; completely positive semidefinite matrix; completely positive matrix
Data: 24-Jul-2022
Editora: Society for Industrial and Applied Mathematics
Projeto: UIDB/0032/2020 
JSPS Grant-in-Aid for Early-Career Scientists grant JP19K20217 and the Grant-in-Aid for Scientific Research (B) grant JP21H03398. 
Título da revista, periódico, livro ou evento: SIAM Journal on Matrix Analysis and Applications
Volume: 44
Número: 3
Resumo: 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.
Descrição: 27 pages, 4 figures. Some minor fixes. To appear at the SIAM Journal on Matrix Analysis
URI: https://hdl.handle.net/10316/114554
ISSN: 0895-4798
1095-7162
DOI: 10.1137/22M1519869
Direitos: openAccess
Aparece nas coleções:I&D CMUC - Artigos em Revistas Internacionais
FCTUC Matemática - Artigos em Revistas Internacionais

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