A variational approach of the rank function

A variational approach of the rank function

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Article ID: iaor20134315
Volume: 21
Issue: 2
Start Page Number: 207
End Page Number: 240
Publication Date: Jul 2013
Journal: TOP
Authors: ,
Keywords: calculus of variations
Abstract:

In the same spirit as the one of the paper (Hiriart‐Urruty and Malick, 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.

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