Optimization Letters

, Volume 7, Issue 4, pp 731–743 | Cite as

Generalized subdifferentials of the rank function

  • Hai Yen LeEmail author
Original Paper


We give an explicit formula for the generalized subdifferentials; i.e. the proximal subdifferential, the Fréchet subdifferential, the limitting subdifferential and the Clarke subdifferential of the counting function. Then, thanks to theorems of A.S. Lewis and H.S. Sendov, we obtain the corresponding generalized subdifferentials of the rank function.


Generalized subdifferentials Rank function Counting function 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institut de mathématiques de ToulouseUniversité Paul Sabatier (Toulouse III)Toulouse Cedex 09France

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