Local convergence of the steepest descent method in Hilbert spaces

Smyrlis, G; Zisis, V

dc.contributor.author	Smyrlis, G	en
dc.contributor.author	Zisis, V	en
dc.date.accessioned	2014-03-01T01:20:44Z
dc.date.available	2014-03-01T01:20:44Z
dc.date.issued	2004	en
dc.identifier.issn	0022-247X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16025
dc.subject	Locally Lipschitz continuous operator	en
dc.subject	Palais-Smale condition	en
dc.subject	Picard-Lindelöf theorem	en
dc.subject	Sobolev embedding theorem	en
dc.subject	Steepest descent method	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	UNCONSTRAINED OPTIMIZATION	en
dc.subject.other	ALGORITHM	en
dc.title	Local convergence of the steepest descent method in Hilbert spaces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jmaa.2004.06.051	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jmaa.2004.06.051	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	The aim of this paper is to establish the local convergence of the steepest descent method for C-1- functionals f :H-->R defined on an infinite-dimensional Hilbert space H, under a Palais-Smaletype condition. The functionals f under consideration are also assumed to have a locally Lipschitz continuous gradient operator delf. Our approach is based on the solutions of the ordinary differential equation x (t) = -del f (x(t)). (C) 2004 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Mathematical Analysis and Applications	en
dc.identifier.doi	10.1016/j.jmaa.2004.06.051	en
dc.identifier.isi	ISI:000225417700014	en
dc.identifier.volume	300	en
dc.identifier.issue	2	en
dc.identifier.spage	436	en
dc.identifier.epage	453	en