Representations of epi-Lipschitzian sets
Optimization and Control
2009-03-05 v1
Abstract
A closed subset of a Banach space 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 , wich Clarke's generalized gradient does not contain 0 at points in the boundary of , 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
Keywords
Cite
@article{arxiv.0903.0711,
title = {Representations of epi-Lipschitzian sets},
author = {Marc-Olivier Czarnecki and Anastasia Nikolaevna Gudovich},
journal= {arXiv preprint arXiv:0903.0711},
year = {2009}
}