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Local Lipschitz Constants and Maximal Subdifferentials

Borwein, Jonathan M. and Vanderwerff, Jon D. and Wang, Shawn Xianfu (2003) Local Lipschitz Constants and Maximal Subdifferentials. Set-Valued Analysis, 11 . pp. 37-67. ISSN 0927-6947

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      Abstract

      It is shown that if $k(x)$ is upper semicontinuous and quasi lower semicontinuou s on a Banach space $X$, then $k(x) B_{X^*}$ is the Clarke subdifferential of some locally Lipschitz function on $X$. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its `local Lipschitz constant' function. Finally, some results concerning the calculus of local Lipschitz constants are developed.

      Item Type: Article
      Additional Information: pubdom TRUE
      Uncontrolled Keywords: Lipschitz function,Baire category,Clarke subdifferential,approximate subdifferential,local Lipschitz-constant function
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      54-xx General topology > 54Exx Spaces with richer structures
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 20 Nov 2003
      Last Modified: 13 Jan 2015 11:48
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/55

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