A note on the differentiability of conjugate functions
type: Item
instance of: scholarly article
title: A note on the differentiability of conjugate functions
zbMATH Open document ID: 1184.26007
author: Thomas Strömberg
published in: Archiv der Mathematik
publication date: 2009-12-14T00:00:00Z
review text: The following extension of Rockafellar's fundamental theorem is proved: Let \(f:\mathbb{R}^n\to\overline{\mathbb{R}}\) be a proper, lower semicontinuous function such that its conjugate \(f^{\ast}\) is proper. Then \(f^{\ast}\) is essentially differentiable if and only if \(f\) is essentially strictly convex.
reviewed by: Tomasz Natkaniec
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 5646238
zbMATH Keywords: Legendre-Fenchel transform
zbMATH Keywords: essential differentiability
zbMATH Keywords: essential strict convexity
MaRDI profile type: Publication
full work available at URL: s00013-009-0050-3
OpenAlex ID: W2094548873
cites work: Fréchet differentiability of convex functions
cites work: Gradients of Convex Functions
cites work: On Conjugate Convex Functions
cites work: Q5295627
cites work: Q3961832
cites work: Convex Analysis
cites work: Variational Analysis
cites work: Duality for nonconvex optimization and its applications
cites work: The Hopf-Lax formula gives the unique viscosity solution
DOI: 10.1007/S00013-009-0050-3
description: scientific article; zbMATH DE number 5646238