Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/9486 |
Resumo: | In this work, we propose and analyze some methods to solve constrained nonlinear systems of equations. First, we present a method that combines the inexact Newton-like method with a specialized version of the conditional gradient method (also known as Frank-Wolfe method). Using a majorant condition, which allows us to prove in a unified way convergence results for some classes functions, the local convergence of the proposed method as well as results on its rates are established. Second, we present a global version of the previous method by means of a derivative-free and nonmonotone line search strategy. Under appropriate conditions the global convergence of the proposed method is proved. Third, based on the well-known Levenberg-Marquardt method, we also propose a Levenberg-Marquardt method with inexact projections which combines the unconstrained Levenberg-Marquardt method with a notion of inexact projetions. In this case, the local convergence of the proposed method is proved using the error bound condition that is weaker than the standard condition full-rank of the Jacobian. Moreover, we also present a global version of the latter method by means of a nonmonotone line search technique. Finally, numerical experiments are also reported to illustrate the performances of the proposed schemes. |
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Gonçalves, Max Leandro Nobrehttp://lattes.cnpq.br/7841103869154032Melo, Jefferson Divino Gonçalves deFerreira, Orizon PereiraGonçalves, Douglas SoaresHaeser, GabrielAndreani, Robertohttp://lattes.cnpq.br/5988282255296542Oliveira, Fabrícia Rodrigues de2019-04-15T12:51:54Z2019-03-26OLIVEIRA, F. R. Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections. 2019. 76 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/9486In this work, we propose and analyze some methods to solve constrained nonlinear systems of equations. First, we present a method that combines the inexact Newton-like method with a specialized version of the conditional gradient method (also known as Frank-Wolfe method). Using a majorant condition, which allows us to prove in a unified way convergence results for some classes functions, the local convergence of the proposed method as well as results on its rates are established. Second, we present a global version of the previous method by means of a derivative-free and nonmonotone line search strategy. Under appropriate conditions the global convergence of the proposed method is proved. Third, based on the well-known Levenberg-Marquardt method, we also propose a Levenberg-Marquardt method with inexact projections which combines the unconstrained Levenberg-Marquardt method with a notion of inexact projetions. In this case, the local convergence of the proposed method is proved using the error bound condition that is weaker than the standard condition full-rank of the Jacobian. Moreover, we also present a global version of the latter method by means of a nonmonotone line search technique. Finally, numerical experiments are also reported to illustrate the performances of the proposed schemes.Neste trabalho, propomos e analisamos alguns métodos para resolver sistemas de equações não lineares com restrições. Primeiro, apresentamos um método que combina o método do tipo Newton inexato com uma versão especializada do método do gradiente condicional (também conhecido como método de Frank-Wolfe). Usando uma condição majorante, a qual permite provar de uma maneira unificada, resultados de convergência para algumas classes de funções, a convergência local do proposto método bem como resultados sobre suas taxas são estabelecidos. Segundo, apresentamos uma versão global do método anterior por meio de uma estratégia de busca linear livre de derivadas e não monótona. Sob condições apropriadas a convergência global do proposto método é provada. Terceiro, baseados no bem conhecido método de Levenberg-Marquardt, também propomos um método de Levenberg-Marquardt com projeções inexatas, o qual combina o método de Levenberg-Marquardt irrestrito com uma noção de projeções inexatas. Neste caso, a convergência local do proposto método é provada usando uma condição de erro limite que é mais fraca que a condição padrão de posto completo da Jacobiana. Além disso, também apresentamos uma versão global do último método por meio de uma técnica de busca linear não monótona. Finalmente, experimentos numéricos são também relatados para ilustrar os desempenhos dos métodos propostos.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2019-04-15T12:10:45Z No. of bitstreams: 2 Tese - Fabrícia Rodrigues de Oliveira - 2019.pdf: 5665011 bytes, checksum: 79f13a4d4406143bb701ba9f1bffba9b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2019-04-15T12:51:54Z (GMT) No. of bitstreams: 2 Tese - Fabrícia Rodrigues de Oliveira - 2019.pdf: 5665011 bytes, checksum: 79f13a4d4406143bb701ba9f1bffba9b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2019-04-15T12:51:54Z (GMT). No. of bitstreams: 2 Tese - Fabrícia Rodrigues de Oliveira - 2019.pdf: 5665011 bytes, checksum: 79f13a4d4406143bb701ba9f1bffba9b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2019-03-26Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessConstrained nonlinear systemsInexact Newton-like conditional gradient methodNonmonotone and derivative-free line searchInexact projectionsLocal and global convergenceSistemas não lineares restritosMétodo do tipo Newton gradiente condicionalEstratégia de busca não monótona e livre de derivadasProjeções inexatasConvergência local e globalCIENCIAS EXATAS E DA TERRA::MATEMATICAMethods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projectionsMétodo para sistemas não lineares restritos: tipo Newton gradiente condicional inexato e Levenberg-Marquardt com projeções inexatasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis6600717948137941247600600600600-4268777512335152015-70908234179844016942075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
dc.title.alternative.por.fl_str_mv |
Método para sistemas não lineares restritos: tipo Newton gradiente condicional inexato e Levenberg-Marquardt com projeções inexatas |
title |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
spellingShingle |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections Oliveira, Fabrícia Rodrigues de Constrained nonlinear systems Inexact Newton-like conditional gradient method Nonmonotone and derivative-free line search Inexact projections Local and global convergence Sistemas não lineares restritos Método do tipo Newton gradiente condicional Estratégia de busca não monótona e livre de derivadas Projeções inexatas Convergência local e global CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
title_full |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
title_fullStr |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
title_full_unstemmed |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
title_sort |
Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections |
author |
Oliveira, Fabrícia Rodrigues de |
author_facet |
Oliveira, Fabrícia Rodrigues de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Gonçalves, Max Leandro Nobre |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/7841103869154032 |
dc.contributor.referee1.fl_str_mv |
Melo, Jefferson Divino Gonçalves de |
dc.contributor.referee2.fl_str_mv |
Ferreira, Orizon Pereira |
dc.contributor.referee3.fl_str_mv |
Gonçalves, Douglas Soares |
dc.contributor.referee4.fl_str_mv |
Haeser, Gabriel |
dc.contributor.referee5.fl_str_mv |
Andreani, Roberto |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5988282255296542 |
dc.contributor.author.fl_str_mv |
Oliveira, Fabrícia Rodrigues de |
contributor_str_mv |
Gonçalves, Max Leandro Nobre Melo, Jefferson Divino Gonçalves de Ferreira, Orizon Pereira Gonçalves, Douglas Soares Haeser, Gabriel Andreani, Roberto |
dc.subject.eng.fl_str_mv |
Constrained nonlinear systems Inexact Newton-like conditional gradient method Nonmonotone and derivative-free line search Inexact projections Local and global convergence |
topic |
Constrained nonlinear systems Inexact Newton-like conditional gradient method Nonmonotone and derivative-free line search Inexact projections Local and global convergence Sistemas não lineares restritos Método do tipo Newton gradiente condicional Estratégia de busca não monótona e livre de derivadas Projeções inexatas Convergência local e global CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.por.fl_str_mv |
Sistemas não lineares restritos Método do tipo Newton gradiente condicional Estratégia de busca não monótona e livre de derivadas Projeções inexatas Convergência local e global |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work, we propose and analyze some methods to solve constrained nonlinear systems of equations. First, we present a method that combines the inexact Newton-like method with a specialized version of the conditional gradient method (also known as Frank-Wolfe method). Using a majorant condition, which allows us to prove in a unified way convergence results for some classes functions, the local convergence of the proposed method as well as results on its rates are established. Second, we present a global version of the previous method by means of a derivative-free and nonmonotone line search strategy. Under appropriate conditions the global convergence of the proposed method is proved. Third, based on the well-known Levenberg-Marquardt method, we also propose a Levenberg-Marquardt method with inexact projections which combines the unconstrained Levenberg-Marquardt method with a notion of inexact projetions. In this case, the local convergence of the proposed method is proved using the error bound condition that is weaker than the standard condition full-rank of the Jacobian. Moreover, we also present a global version of the latter method by means of a nonmonotone line search technique. Finally, numerical experiments are also reported to illustrate the performances of the proposed schemes. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-04-15T12:51:54Z |
dc.date.issued.fl_str_mv |
2019-03-26 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
OLIVEIRA, F. R. Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections. 2019. 76 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/9486 |
identifier_str_mv |
OLIVEIRA, F. R. Methods for constrained nonlinear systems: inexact Newton-like conditional gradient and Levenberg-Marquardt with inexact projections. 2019. 76 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/9486 |
dc.language.iso.fl_str_mv |
por |
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por |
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6600717948137941247 |
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600 600 600 600 |
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-7090823417984401694 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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Programa de Pós-graduação em Matemática (IME) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
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