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Generalized subdifferentials of the rank function

Abstract

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.

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Correspondence to Hai Yen Le.

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Le, H.Y. Generalized subdifferentials of the rank function. Optim Lett 7, 731–743 (2013). https://doi.org/10.1007/s11590-012-0456-x

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  • DOI: https://doi.org/10.1007/s11590-012-0456-x

Keywords

  • Generalized subdifferentials
  • Rank function
  • Counting function