Subdifferential and Properties of Convex Functions with Respect to Vector Fields - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Convex Analysis Année : 2014

Subdifferential and Properties of Convex Functions with Respect to Vector Fields

Résumé

We study properties of functions convex with respect to a given family χ of vector fields, a notion that appears natural in Carnot-Carathéodory metric spaces. We define a suitable subdifferential and show that a continuous function is χ-convex if and only if such subdifferential is nonempty at every point. For vector fields of Carnot type we deduce from this property that a generalized Fenchel transform is involutive and a weak form of Jensen inequality. Finally we introduce and compare several notions of χ-affine functions and show their connections with χ-convexity.
Fichier non déposé

Dates et versions

hal-00916081 , version 1 (09-12-2013)

Identifiants

  • HAL Id : hal-00916081 , version 1

Citer

Martino Bardi, Federica Dragoni. Subdifferential and Properties of Convex Functions with Respect to Vector Fields. Journal of Convex Analysis, 2014, 21 (3), pp.785--810. ⟨hal-00916081⟩

Collections

SADCO TDS-MACS
225 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More