Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds
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/9507 |
Resumo: | In this thesis, we will study three versions of the Newton method for solving problems in two contexts, namely Euclidean and Riemannian. In the Euclidean context, we will present the Newton method with feasible inexact projections for solving generalized equations subject to a set of constraints. Under local assumptions, the linear or superlinear convergence of a sequence generated by the proposed method is established. Next, a version of the inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations is presented. Using suitable assumptions, the linear or superlinear convergence of a sequence generated by the method is proved. Furthermore, to illustrate the practical behavior of the proposed method, some numerical experiments are reported. Under another perspective, the last version of the Newton method to be investigated is an extension of the nonsmooth Newton method itself from the Euclidean context to the Riemannian, objecting to find a singularity of a special class of locally Lipschitz continuous vector fields. In particular, this method retrieves the classical nonsmooth Newton method to solve a system of nonsmooth equations. The well-definedness of the sequence generated by the method is ensured and the convergence analysis of the method is made under local and semi-local assumptions. |
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Ferreira, Orizon Pereirahttp://lattes.cnpq.br/0201145506453251Prudente, Leandro da FonsecaGonçalves, Max Leandro NobreAndreani, RobertoHaeser, GabrielGonçalves, Douglas Soareshttp://lattes.cnpq.br/8929908824371424Oliveira, Fabiana Rodrigues de2019-04-18T16:40:47Z2019-03-27OLIVEIRA, F. R. Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds. 2019. 71 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/9507In this thesis, we will study three versions of the Newton method for solving problems in two contexts, namely Euclidean and Riemannian. In the Euclidean context, we will present the Newton method with feasible inexact projections for solving generalized equations subject to a set of constraints. Under local assumptions, the linear or superlinear convergence of a sequence generated by the proposed method is established. Next, a version of the inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations is presented. Using suitable assumptions, the linear or superlinear convergence of a sequence generated by the method is proved. Furthermore, to illustrate the practical behavior of the proposed method, some numerical experiments are reported. Under another perspective, the last version of the Newton method to be investigated is an extension of the nonsmooth Newton method itself from the Euclidean context to the Riemannian, objecting to find a singularity of a special class of locally Lipschitz continuous vector fields. In particular, this method retrieves the classical nonsmooth Newton method to solve a system of nonsmooth equations. The well-definedness of the sequence generated by the method is ensured and the convergence analysis of the method is made under local and semi-local assumptions.Nesta tese, estudaremos três versões do método de Newton para resolver problemas em dois contextos, a saber, Euclidiano e Riemanniano. No contexto Euclidiano, apresentaremos o método de Newton com projeções inexatas viáveis para resolver equações generalizadas sujeitas à um conjunto de restrições. Sob hipóteses locais, a convergência linear ou superlinear de uma sequência gerada pelo método proposto é estabelecida. Em seguida, uma versão do método de Newton inexato com projeções inexatas viáveis para resolver equações restritas diferenciáveis e não-diferenciáveis é apresentada. Usando hipóteses adequadas, a convergência linear ou superlinear de uma sequência gerada pelo método é provada. Além disso, para ilustrar o comportamento prático do método, alguns experimentos numéricos são reportados. Sob uma outra perspectiva, a última versão do método de Newton a ser investigada é uma extensão do próprio método de Newton não-diferenciável do contexto Euclidiano para o Riemanniano, objetivando encontrar uma singularidade de uma classe especial de campos de vetores localmente Lipschitz contínuos. Em particular, este método recupera o clássico método de Newton não-diferenciável para resolver um sistema de equações não-diferenciáveis. A boa definição da sequência gerada pelo método é garantida e a análise de convergência do método é feita sob hipóteses locais e semi-locais.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2019-04-18T13:49:46Z No. of bitstreams: 2 Tese - Fabiana Rodrigues de Oliveira - 2019.pdf: 5623260 bytes, checksum: 87b9b63c64e8f16cdeb5051e1d8eed00 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2019-04-18T16:40:47Z (GMT) No. of bitstreams: 2 Tese - Fabiana Rodrigues de Oliveira - 2019.pdf: 5623260 bytes, checksum: 87b9b63c64e8f16cdeb5051e1d8eed00 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2019-04-18T16:40:47Z (GMT). No. of bitstreams: 2 Tese - Fabiana Rodrigues de Oliveira - 2019.pdf: 5623260 bytes, checksum: 87b9b63c64e8f16cdeb5051e1d8eed00 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2019-03-27Coordenação 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/openAccessProjeção inexata viávelFeasible inexact projectionRiemannian manifoldsVector fieldsConvergence analysisMédodo de NewtonNewton methodVariedades riemannianasCampos de vetoresAnálise de convergênciaCIENCIAS EXATAS E DA TERRA::MATEMATICANewton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifoldsMétodo de Newton com projeções inexatas para equações restritas e método de Newton não-diferenciável em variedades riemannianasinfo: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 |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
dc.title.alternative.por.fl_str_mv |
Método de Newton com projeções inexatas para equações restritas e método de Newton não-diferenciável em variedades riemannianas |
title |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
spellingShingle |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds Oliveira, Fabiana Rodrigues de Projeção inexata viável Feasible inexact projection Riemannian manifolds Vector fields Convergence analysis Médodo de Newton Newton method Variedades riemannianas Campos de vetores Análise de convergência CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
title_full |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
title_fullStr |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
title_full_unstemmed |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
title_sort |
Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds |
author |
Oliveira, Fabiana Rodrigues de |
author_facet |
Oliveira, Fabiana Rodrigues de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Ferreira, Orizon Pereira |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0201145506453251 |
dc.contributor.referee1.fl_str_mv |
Prudente, Leandro da Fonseca |
dc.contributor.referee2.fl_str_mv |
Gonçalves, Max Leandro Nobre |
dc.contributor.referee3.fl_str_mv |
Andreani, Roberto |
dc.contributor.referee4.fl_str_mv |
Haeser, Gabriel |
dc.contributor.referee5.fl_str_mv |
Gonçalves, Douglas Soares |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/8929908824371424 |
dc.contributor.author.fl_str_mv |
Oliveira, Fabiana Rodrigues de |
contributor_str_mv |
Ferreira, Orizon Pereira Prudente, Leandro da Fonseca Gonçalves, Max Leandro Nobre Andreani, Roberto Haeser, Gabriel Gonçalves, Douglas Soares |
dc.subject.eng.fl_str_mv |
Projeção inexata viável Feasible inexact projection Riemannian manifolds Vector fields Convergence analysis |
topic |
Projeção inexata viável Feasible inexact projection Riemannian manifolds Vector fields Convergence analysis Médodo de Newton Newton method Variedades riemannianas Campos de vetores Análise de convergência CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.por.fl_str_mv |
Médodo de Newton Newton method Variedades riemannianas Campos de vetores Análise de convergência |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this thesis, we will study three versions of the Newton method for solving problems in two contexts, namely Euclidean and Riemannian. In the Euclidean context, we will present the Newton method with feasible inexact projections for solving generalized equations subject to a set of constraints. Under local assumptions, the linear or superlinear convergence of a sequence generated by the proposed method is established. Next, a version of the inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations is presented. Using suitable assumptions, the linear or superlinear convergence of a sequence generated by the method is proved. Furthermore, to illustrate the practical behavior of the proposed method, some numerical experiments are reported. Under another perspective, the last version of the Newton method to be investigated is an extension of the nonsmooth Newton method itself from the Euclidean context to the Riemannian, objecting to find a singularity of a special class of locally Lipschitz continuous vector fields. In particular, this method retrieves the classical nonsmooth Newton method to solve a system of nonsmooth equations. The well-definedness of the sequence generated by the method is ensured and the convergence analysis of the method is made under local and semi-local assumptions. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-04-18T16:40:47Z |
dc.date.issued.fl_str_mv |
2019-03-27 |
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. Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds. 2019. 71 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/9507 |
identifier_str_mv |
OLIVEIRA, F. R. Newton method with feasible inexact projections for constrained equations and nonsmooth Newton method in Riemannian manifolds. 2019. 71 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/9507 |
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/ |
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openAccess |
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Universidade Federal de Goiás |
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Programa de Pós-graduação em Matemática (IME) |
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UFG |
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Brasil |
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Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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