Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/114554
Title: | Self-dual polyhedral cones and their slack matrices | Authors: | Gouveia, João Lourenço, Bruno F. |
Keywords: | self-dual cone; slack matrix; polyhedral cone; polytope; doubly nonnegative matrix; completely positive semidefinite matrix; completely positive matrix | Issue Date: | 24-Jul-2022 | Publisher: | Society for Industrial and Applied Mathematics | Project: | info:eu-repo/grantAgreement/UIDB/00324/2020 | Serial title, monograph or event: | SIAM Journal on Matrix Analysis and Applications | Volume: | 44 | Issue: | 3 | 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. | Description: | 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 | Rights: | openAccess |
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 |
Page view(s)
310
checked on Sep 25, 2024
Download(s)
303
checked on Sep 25, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.