Acta Mathematica Vietnamica

, Volume 40, Issue 4, pp 735–746 | Cite as

The Viscosity Subdifferential of the Rank Function via the Corresponding Subdifferential of its Moreau Envelopes

  • Jean-Baptiste Hiriart-Urruty
  • Hai Yen LeEmail author


We derive the so-called viscosity subdifferential of the rank function via a limiting process applied to the Moreau envelopes of the rank function. Before that, we obtain the explicit expressions of all the generalized subdifferentials of the Moreau envelopes of the rank function.


Rank function Singular values of a matrix Moreau envelopes Generalized subdifferentials Viscosity subdifferential 

Mathematics Subject Classification (2010)

15A 46N10 65K10 90C 



We would like to thank Prof. A. Jourani (University of Bourgogne, Dijon) for drawing our attention to this possible way of getting at the Fréchet generalized subdifferential of the rank function (ALEL meeting in Castro-Urdiales, June 2011).


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Institute of MathematicsPaul Sabatier UniversityToulouseFrance
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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