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arXiv · 0903.0711

Representations of epi-Lipschitzian sets

Marc-Olivier Czarnecki·Anastasia Nikolaevna Gudovich
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Abstract

A closed subset $M$ of a Banach space $E$ is \ep, i.e., can be represented locally as the epigraph of a Lipschitz function, if and only if it is the level set of some locally Lipschitz function $f: E\to \R$, wich Clarke's generalized gradient does not contain 0 at points in the boundary of $M$, i.e., such that: M=\{x \mid f(x)\leq 0\}, 0\not \in \partial f(x) {if} x\in \bd M. This extends the characterization previously known in finite dimension and answers to a standing open question

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Marc-Olivier Czarnecki, Anastasia Nikolaevna Gudovich. 2009-03-04. Representations of epi-Lipschitzian sets. https://arxiv.org/abs/0903.0711

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