# 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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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.