On the method of the steepest, descent

Let H be a Hilbert space over the reals and let f: H → R1 be a function of class C1.  We have shown in |1|  that the differential equationdu/dt= -T (u(t) ),u(0)= uo                                                                                                                                        ...

Full description

Autores:
Restrepo, Guillermo
Tipo de recurso:
Article of journal
Fecha de publicación:
1968
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/42043
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/42043
http://bdigital.unal.edu.co/32140/
Palabra clave:
Ecuaciones diferencias
números reales
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_52b6b588748b08dcd8389f13e0a4715d
oai_identifier_str oai:repositorio.unal.edu.co:unal/42043
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Restrepo, Guillermoac5eb35a-f00f-4a62-8914-d991b0671d463002019-06-28T10:28:32Z2019-06-28T10:28:32Z1968https://repositorio.unal.edu.co/handle/unal/42043http://bdigital.unal.edu.co/32140/Let H be a Hilbert space over the reals and let f: H → R1 be a function of class C1.  We have shown in |1|  that the differential equationdu/dt= -T (u(t) ),u(0)= uo                                                                                                                                               (1)(T = grad f) has global solutions if i) ≥ c||x-y ||2 , c and gt; 0,ii) f is bounded from below;iii) T is locally Lipschitzian. To be precise, in [1;Th.3] we heve assumed f to be of class C2 and f" to be locally bounded. However, the hypothesis  f"  is locally bounded implies that  f'´ = T is locally Lipschitzian, and this is what matters to show existence and uniqueness.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/31495Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 2, núm. 2 (1968); 45-49 0034-7426Restrepo, Guillermo (1968) On the method of the steepest, descent. Revista Colombiana de Matemáticas; Vol. 2, núm. 2 (1968); 45-49 0034-7426 .On the method of the steepest, descentArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTEcuaciones diferenciasnúmeros realesORIGINAL31495-114357-1-PB.pdfapplication/pdf1133190https://repositorio.unal.edu.co/bitstream/unal/42043/1/31495-114357-1-PB.pdf47b43fd28f966da72e85f1e0ab2b1db0MD51THUMBNAIL31495-114357-1-PB.pdf.jpg31495-114357-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg7548https://repositorio.unal.edu.co/bitstream/unal/42043/2/31495-114357-1-PB.pdf.jpg2f0e66820de6e0ef27896cc3e1d561aeMD52unal/42043oai:repositorio.unal.edu.co:unal/420432024-02-03 23:06:34.36Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv On the method of the steepest, descent
title On the method of the steepest, descent
spellingShingle On the method of the steepest, descent
Ecuaciones diferencias
números reales
title_short On the method of the steepest, descent
title_full On the method of the steepest, descent
title_fullStr On the method of the steepest, descent
title_full_unstemmed On the method of the steepest, descent
title_sort On the method of the steepest, descent
dc.creator.fl_str_mv Restrepo, Guillermo
dc.contributor.author.spa.fl_str_mv Restrepo, Guillermo
dc.subject.proposal.spa.fl_str_mv Ecuaciones diferencias
números reales
topic Ecuaciones diferencias
números reales
description Let H be a Hilbert space over the reals and let f: H → R1 be a function of class C1.  We have shown in |1|  that the differential equationdu/dt= -T (u(t) ),u(0)= uo                                                                                                                                               (1)(T = grad f) has global solutions if i) ≥ c||x-y ||2 , c and gt; 0,ii) f is bounded from below;iii) T is locally Lipschitzian. To be precise, in [1;Th.3] we heve assumed f to be of class C2 and f" to be locally bounded. However, the hypothesis  f"  is locally bounded implies that  f'´ = T is locally Lipschitzian, and this is what matters to show existence and uniqueness.
publishDate 1968
dc.date.issued.spa.fl_str_mv 1968
dc.date.accessioned.spa.fl_str_mv 2019-06-28T10:28:32Z
dc.date.available.spa.fl_str_mv 2019-06-28T10:28:32Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.coarversion.spa.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
format http://purl.org/coar/resource_type/c_6501
status_str publishedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/42043
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/32140/
url https://repositorio.unal.edu.co/handle/unal/42043
http://bdigital.unal.edu.co/32140/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/31495
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 2, núm. 2 (1968); 45-49 0034-7426
dc.relation.references.spa.fl_str_mv Restrepo, Guillermo (1968) On the method of the steepest, descent. Revista Colombiana de Matemáticas; Vol. 2, núm. 2 (1968); 45-49 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/42043/1/31495-114357-1-PB.pdf
https://repositorio.unal.edu.co/bitstream/unal/42043/2/31495-114357-1-PB.pdf.jpg
bitstream.checksum.fl_str_mv 47b43fd28f966da72e85f1e0ab2b1db0
2f0e66820de6e0ef27896cc3e1d561ae
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
_version_ 1814089567049875456

Publicaciones similares