A variational approach of the rank function

Jean-Baptiste Hiriart-Urruty (1) , Hai Yen Le (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Rank of matrix; Optimization; Nonsmooth analysis; Moreau-Yosida regularization; Generalized subdifferentials

Domaines: Mathématiques [math]

Jean-Baptiste Hiriart-Urruty, Hai Yen Le. A variational approach of the rank function. TOP, 2013, 21 (2), pp.207-240. ⟨10.1007/s11750-013-0283-y⟩. ⟨hal-00966090⟩