A variational approach of the rank function

Jean-Baptiste Hiriart-Urruty () and Hai Le ()

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2013, vol. 21, issue 2, 207-240

Abstract: In the same spirit as the one of the paper (Hiriart-Urruty and Malick in J. Optim. Theory Appl. 153(3):551–577, 2012 ) on positive semidefinite matrices, we survey several useful properties of the rank function (of a matrix) and add some new ones. Since the so-called rank minimization problems are the subject of intense studies, we adopt the viewpoint of variational analysis, that is the one considering all the properties useful for optimizing, approximating or regularizing the rank function. Copyright Sociedad de Estadística e Investigación Operativa 2013

Keywords: Rank of matrix; Optimization; Nonsmooth analysis; Moreau–Yosida regularization; Generalized subdifferentials; 49-02; 65K10 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11750-013-0283-y

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