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Subdifferential and properties of convex functions with respect to vector fields

Bardi, Martino and Dragoni, Federica 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
Last Modified: 04 Jun 2017 08:15
URI: http://orca.cf.ac.uk/id/eprint/75018

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