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Lipschitz Functions with Maximal Clarke Subdifferentials Are Generic

Borwein, Jonathan M. and Wang, Shawn Xianfu (2000) Lipschitz Functions with Maximal Clarke Subdifferentials Are Generic. Proceedings of the American Mathematical Society, 128 . pp. 3221-3230. ISSN 0002-9939

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      Abstract

      We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Lipschitz function, Clarke subdifferential, separable Banach spaces, Baire category, partial ordering, Banach lattice, approximate subdifferential
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      54-xx General topology > 54Exx Spaces with richer structures
      26-xx Real functions > 26Exx Miscellaneous topics
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 13 Jan 2015 12:28
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/206

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