An enhanced baillon-haddad theorem for convex functions defined on convex sets

UOH Academic Repository

dc.contributor.author	Pérez-Aros, P
dc.contributor.author	Vilches, E
dc.date.accessioned	2024-01-17T15:53:59Z
dc.date.available	2024-01-17T15:53:59Z
dc.date.issued	2021
dc.identifier.uri	https://repositorio.uoh.cl/handle/611/311
dc.description.abstract	The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is beta-Lipschitz if and only if it is 1/beta-cocoercive. In this paper, we extend this theorem to Gateaux differentiable and lower semicontinuous convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of C1,+ convex functions in terms of local cocoercivity.
dc.description.sponsorship	CONICYT Chile under grant Fondecyt de Iniciacion
dc.description.sponsorship	CONICYT Chile under grant Fondecyt regular(Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)CONICYT FONDECYT)
dc.relation.uri	http://dx.doi.org/10.1007/s00245-019-09626-6
dc.subject	Convex function
dc.subject	Cocoercivity
dc.subject	Lipschitz function
dc.subject	Nonexpansive operator
dc.subject	Baillon-Haddad Theorem
dc.title	An enhanced baillon-haddad theorem for convex functions defined on convex sets
dc.type	Artículo
uoh.revista	APPLIED MATHEMATICS AND OPTIMIZATION
dc.identifier.doi	10.1007/s00245-019-09626-6
dc.citation.volume	83
dc.citation.issue	3
dc.identifier.orcid	Perez-Aros, Pedro/0000-0002-8756-3011
dc.identifier.orcid	Vilches, Emilio/0000-0002-4387-9313
uoh.indizacion	Web of Science