On the Newton method for set-valued maps

Detalhes bibliográficos
Autor(a) principal: Dias, Susana
Data de Publicação: 2012
Outros Autores: Smirnov, Georgi
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/14845
Resumo: The Newton method is one of the most powerful tools used to solve systems of nonlinear equations. Its set-valued generalization, considered in this work, allows one to solve also nonlinear equations with geometric constraints and systems of inequalities in a unified manner. The emphasis is given to systems of linear inequalities. The study of the wellposedness of the algorithm and of its convergence is fulfilled in the framework of modern variational analysis.
id RCAP_026c7a7e139cf9a906608499e6b9e97f
oai_identifier_str oai:repositorium.sdum.uminho.pt:1822/14845
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling On the Newton method for set-valued mapsNewton’s methodSet-valued mapsVariational analysisScience & TechnologyThe Newton method is one of the most powerful tools used to solve systems of nonlinear equations. Its set-valued generalization, considered in this work, allows one to solve also nonlinear equations with geometric constraints and systems of inequalities in a unified manner. The emphasis is given to systems of linear inequalities. The study of the wellposedness of the algorithm and of its convergence is fulfilled in the framework of modern variational analysis.The authors are grateful to Oleg Burdakov, Boris Mordukhovich, and Vera Roshchina for their valuable comments. This research was supported by the Portuguese Foundation for Science and Technologies (FCT), the Portuguese Operational Programme for Competitiveness Factors (COMPETE), the Portuguese National Strategic Reference Framework (QREN), and the European Regional Development Fund (FEDER).ElsevierUniversidade do MinhoDias, SusanaSmirnov, Georgi2012-032012-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/14845eng0362-546X10.1016/j.na.2011.04.005info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:06:31Zoai:repositorium.sdum.uminho.pt:1822/14845Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:57:13.651972Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the Newton method for set-valued maps
title On the Newton method for set-valued maps
spellingShingle On the Newton method for set-valued maps
Dias, Susana
Newton’s method
Set-valued maps
Variational analysis
Science & Technology
title_short On the Newton method for set-valued maps
title_full On the Newton method for set-valued maps
title_fullStr On the Newton method for set-valued maps
title_full_unstemmed On the Newton method for set-valued maps
title_sort On the Newton method for set-valued maps
author Dias, Susana
author_facet Dias, Susana
Smirnov, Georgi
author_role author
author2 Smirnov, Georgi
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Dias, Susana
Smirnov, Georgi
dc.subject.por.fl_str_mv Newton’s method
Set-valued maps
Variational analysis
Science & Technology
topic Newton’s method
Set-valued maps
Variational analysis
Science & Technology
description The Newton method is one of the most powerful tools used to solve systems of nonlinear equations. Its set-valued generalization, considered in this work, allows one to solve also nonlinear equations with geometric constraints and systems of inequalities in a unified manner. The emphasis is given to systems of linear inequalities. The study of the wellposedness of the algorithm and of its convergence is fulfilled in the framework of modern variational analysis.
publishDate 2012
dc.date.none.fl_str_mv 2012-03
2012-03-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/14845
url http://hdl.handle.net/1822/14845
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0362-546X
10.1016/j.na.2011.04.005
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799132360973746176

Registros relacionados