Characterization of the Clarke regularity of subanalytic sets - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2018

Characterization of the Clarke regularity of subanalytic sets

Résumé

In this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with the set \\ $$\mathcal{L}(A, x_0):= \bigg\{\dot{c}_+(0) \in \mathbb{R}^n: \, c:[0,1]\longrightarrow A\;\;\mbox{\it is Lipschitz}, \, c(0)=x_0\bigg\}.$$ Where $\dot{c}_+(0)$ denotes the right-strict derivative of $c$ at $0$. The results obtained are used to show that the Clarke regularity of the epigraph of a function may be characterized by a new formula of the Clarke subdifferential of that function.

Dates et versions

hal-01666603 , version 1 (18-12-2017)

Identifiants

Citer

Abderrahim Jourani, Moustapha Séne. Characterization of the Clarke regularity of subanalytic sets. Proceedings of the American Mathematical Society, 2018, 146 (4), pp.1639-1649. ⟨10.1090/proc/13847⟩. ⟨hal-01666603⟩
81 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More