Differential properties of the Moreau envelope
| Affiliation auteurs | Affiliation ok |
| Titre | Differential properties of the Moreau envelope |
| Type de publication | Journal Article |
| Year of Publication | 2014 |
| Auteurs | Jourani A, Thibault L, Zagrodny D |
| Journal | JOURNAL OF FUNCTIONAL ANALYSIS |
| Volume | 266 |
| Pagination | 1185-1237 |
| Date Published | FEB 1 |
| Type of Article | Article |
| ISSN | 0022-1236 |
| Mots-clés | Differentiability of the distance function, Directional differentiability of the Moreau envelope, Essentially directionally smooth function, Inf-convolution, Moreau envelope, Subdifferential, Subregular function, Tchebyshev sets |
| Résumé | In a vector space endowed with a uniformly Gateaux 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. (C) 2013 Elsevier Inc. All rights reserved. |
| DOI | 10.1016/j.jfa.2013.11.008 |