Tangent and normal cones for low-rank matrices

dc.contributor.author	Hosseini, Seyedehsomayeh
dc.contributor.author	Luke, D. Russel
dc.contributor.author	Uschmajew, André
dc.date.accessioned	2024-08-13T14:16:45Z
dc.date.available	2024-08-13T14:16:45Z
dc.date.issued	10.2017
dc.identifier.uri	https://hdl.handle.net/20.500.11811/11830
dc.description.abstract	In [D. R. Luke, J. Math. Imaging Vision, 47(3):231-238, 2013] the structure of the Mordukhovich normal cone to varieties of low rank matrices at rank-deficient points has been determined. A simplified proof of that result is presented here. As a corollary we obtain the corresponding Clarke normal cone. The results are put into context of first-order optimality conditions for low-rank matrix optimization problems.	en
dc.format.extent	7
dc.language.iso	eng
dc.relation.ispartofseries	INS Preprints ; 1715
dc.rights	In Copyright
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/
dc.subject	Matrix optimization
dc.subject	Low rank constraint
dc.subject	Optimality conditions
dc.subject.ddc	510 Mathematik
dc.subject.ddc	518 Numerische Analysis
dc.title	Tangent and normal cones for low-rank matrices
dc.type	Preprint
dc.publisher.name	Institut für Numerische Simulation (INS)
dc.publisher.location	Bonn
dc.rights.accessRights	openAccess
dc.relation.doi	https://doi.org/10.1007/978-3-030-11370-4_3
ulbbn.pubtype	Zweitveröffentlichung
dcterms.bibliographicCitation.url	https://ins.uni-bonn.de/publication/preprints

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