On the Newton method for set-valued maps
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
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. |
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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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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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 |
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1799132360973746176 |