Differential properties of the Moreau envelope
Abderrahim Jourani
- Fonction : Auteur
- PersonId : 994822
- IdHAL : abderrahim-jourani
Lionel Thibault
- Fonction : Auteur
- PersonId : 1016652
Résumé
In a vector space endowed with a uniformly Gâteaux differentiable norm, it is proved that the Moreau envelope enjoys many remarkable differential properties and that its subdifferential can be completely described through a certain approximate proximal mapping. This description shows in particular that the Moreau envelope is essentially directionally smooth. New differential properties are derived for the distance function associated with a closed set. Moreover, the analysis, when applied to the investigation of the convexity of Tchebyshev sets, allows us to recover several known results in the literature and to provide some new ones.
Domaines
Mathématiques [math]Format du dépôt | Notice |
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Type de dépôt | Article dans une revue |
Titre |
en
Differential properties of the Moreau envelope
|
Résumé |
en
In a vector space endowed with a uniformly Gâteaux differentiable norm, it is proved that the Moreau envelope enjoys many remarkable differential properties and that its subdifferential can be completely described through a certain approximate proximal mapping. This description shows in particular that the Moreau envelope is essentially directionally smooth. New differential properties are derived for the distance function associated with a closed set. Moreover, the analysis, when applied to the investigation of the convexity of Tchebyshev sets, allows us to recover several known results in the literature and to provide some new ones.
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Auteur(s) |
Abderrahim Jourani
1
, Lionel Thibault
2
, Dariusz Zagrodny
3
1
IMB -
Institut de Mathématiques de Bourgogne [Dijon]
( 1146359 )
- Université de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex
- France
2
I3M -
Institut de Mathématiques et de Modélisation de Montpellier
( 631 )
- Case Courrier 051 Place Eugène Bataillon 34095 MONTPELLIER CEDEX 5
- France
3
UKSW -
Cardinal Stefan Wyszyński University
( 426074 )
- Dewajtis 5, 00-001 Warszawa
- Pologne
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Langue du document |
Anglais
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Nom de la revue |
|
Vulgarisation |
Non
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Comité de lecture |
Oui
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Audience |
Internationale
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Date de publication |
2014-02
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Volume |
266
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Numéro |
3
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Page/Identifiant |
1185-1237
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Domaine(s) |
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DOI | 10.1016/j.jfa.2013.11.008 |
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