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Representations of epi-Lipschitzian sets

โœ Scribed by Marc-Olivier Czarnecki; Anastasia Nikolaevna Gudovich

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
260 KB
Volume
73
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

A closed subset M of a Banach space E is epi-Lipschitzian, 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 โ†’ R, for which Clarke's generalized gradient does not contain 0 at points in the boundary of M, i.e., such that:

This extends the characterization previously known in finite dimension and answers to a standing question.

๐Ÿ“œ SIMILAR VOLUMES

On a class of compactly epi-Lipschitzian
On a class of compactly epi-Lipschitzian sets
โœ Abderrahim Jourani ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 146 KB

The paper is devoted to the study of the so-called compactly epi-Lipschitzian sets. These sets are needed for many aspects of generalized di erentiation, particulary for necessary optimality conditions, stability of mathematical programming problems and calculus rules for subdi erentials and normal

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โœ Mike Develin ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 121 KB

In this paper, we investigate representations of sets of integers as subset sums of other sets of minimal size, achieving results on the nature of the representing set as well as providing several reformulations of the problem. We apply one of these reformulations to prove a conjecture and extend a