Tangent and normal cones for low-rank matrices
Tangent and normal cones for low-rank matrices
View/Date of Publication
10.2017Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
Show full item record
Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11830
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.
Subjects
Matrix optimization, Low rank constraint, Optimality conditions
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/978-3-030-11370-4_3Part of Series
INS Preprints ; 1715Hosseini, Seyedehsomayeh; Luke, D. Russel; Uschmajew, André: Tangent and normal cones for low-rank matrices. In: INS Preprints, 1715.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11830
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11830
@unpublished{handle:20.500.11811/11830,
author = {{Seyedehsomayeh Hosseini} and {D. Russel Luke} and {André Uschmajew}},
title = {Tangent and normal cones for low-rank matrices},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = oct,
INS Preprints},
volume = 1715,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11830}
}
author = {{Seyedehsomayeh Hosseini} and {D. Russel Luke} and {André Uschmajew}},
title = {Tangent and normal cones for low-rank matrices},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = oct,
INS Preprints},
volume = 1715,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11830}
}
The following license files are associated with this item:
