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Characterization of Clarke subgradients among one-dimensional multifunctions

Borwein, Jonathan M. and Fitzpatrick, Simon (1995) Characterization of Clarke subgradients among one-dimensional multifunctions. In: Proceedings of the Optimization Miniconference II, 1995, Univ Ballarat Press.

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      Abstract

      We introduce the notions of an \elsc and an \eusc function of a real variable. The Clarke subgradients of locally Lipschitz functions on an open interval $I$ are shown to be exactly those multifunctions on $I$ of the form $[\alpha(x),\beta(x)]$ where $\alpha$ is \elsc and $\beta$ is \eusc on $I$. The approximate and symmetric subgradients of locally Lipschitz functions on $I$ are also characterized.

      Item Type: Conference or Workshop Item (Paper)
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Clarke subgradient, approximately continuous, locally Lipschitz function, robustly lower semicontinuous, robustly upper semicontinuous, cusco, approximate subgradient, symmetric subgradient, strict differentiability
      Subjects: 49-xx Calculus of variations and optimal control; optimization
      26-xx Real functions
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 27 Oct 2003
      Last Modified: 24 Jul 2015 11:50
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/23

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