Subdifferential and properties of convex functions with respect to vector fields

Bardi, Martino and Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725 2014. Subdifferential and properties of convex functions with respect to vector fields. Journal of Convex Analysis 21 (3) , pp. 785-810.

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Abstract

We study properties of functions convex with respect to a given family X of vector fields, a notion that appears natural in Carnot-Carath ́eodory metric spaces. We define a suitable sub- differential and show that a continuous function is X -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 X-affine functions and show their connections with X-convexity.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Heldermann Verlag
ISSN:	0944-6532
Last Modified:	28 Oct 2022 09:35
URI:	https://orca.cardiff.ac.uk/id/eprint/75018

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