A variational approach of the rank function

Jean-Baptiste Hiriart-Urruty ^[1] ; Hai Yen Le ^[1]
1. [1] Paul Sabatier University
  
  Paul Sabatier University
  
  Arrondissement de Toulouse, Francia
Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 21, Nº. 2, 2013, págs. 207-240
Idioma: inglés
DOI: 10.1007/s11750-013-0283-y
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Resumen
- 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.