A variational approach of the rank function

English

Séminaire Modèles et Algorithmes Déterministes: CASYS

27/11/2012 - 14:00 Mr Jean-Baptiste HIRIART-URRUTY (Université de Toulouse) Petit Amphi de l'INRIA Rhône-Alpes, Montbonnot

In the same spirit as the one in a survey-paper co-authored with J. Malick on positive semidefine matrices ("A fresh variational-analysis look at the positive semidefinite matrices world", J. of Optimization Theory and Applications, 2012), 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. Survey co-authored with Hai Yen Le, Ph D student.