Proximal point methods for multiobjective optimization in riemannian manifolds

Detalhes bibliográficos
Autor(a) principal: Meireles, Lucas Vidal de
Data de Publicação: 2019
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/0013000003bk3
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/9410
Resumo: In this work, two different proximal-type methods are investigated in the Riemannian context, namely, an exact and an inexact version. Two strategies were used to analyze these methods. For the exact version, we used a direct approach by investigating the regularized problem, not considering any convexity assumption over the constraint sets, that determine the vectorial improvement steps, which replaces the classical approach via scalarization. To study the inexact version, a definition of the approximate Pareto efficient solution is introduced. For the convex case on Hadamard manifolds, full convergence of both methods to a weak Pareto optimal point is obtained.
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spelling Bento, Glaydston de Carvalhohttp://lattes.cnpq.br/1089906772427394Bento, Glaydston de CarvalhoOliveira, Paulo RobertoSantos, Paulo Sérgio Marques dosCruz Neto, João Xavier daFerreira, Orizon Pereirahttp://lattes.cnpq.br/9108358595172188Meireles, Lucas Vidal de2019-03-29T13:49:52Z2019-02-26MEIRELES, L. V. Proximal point methods for multiobjective optimization in riemannian manifolds. 2019. 49 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/9410ark:/38995/0013000003bk3In this work, two different proximal-type methods are investigated in the Riemannian context, namely, an exact and an inexact version. Two strategies were used to analyze these methods. For the exact version, we used a direct approach by investigating the regularized problem, not considering any convexity assumption over the constraint sets, that determine the vectorial improvement steps, which replaces the classical approach via scalarization. To study the inexact version, a definition of the approximate Pareto efficient solution is introduced. For the convex case on Hadamard manifolds, full convergence of both methods to a weak Pareto optimal point is obtained.Neste trabalho, dois diferentes métodos tipo-proximal são investigados no contexto Riemanniano, uma versão exata e uma inexata. Duas estratégias foram usadas a fim de analisar estes métodos. Para a versão exata, usamos uma abordagem direta investigando o problema regularizado, não considerando qualquer hipótese de convexidade sobre os conjuntos de restrições, que fornece os passos de melhoria vetorial do subproblema proximal, o qual substitui a abordagem clássica via escalarização. Para estudar a versão inexata introduzimos uma definição de solução Pareto eficiente aproximada. No caso convexo, sobre variedades Hadamard, convergência total de ambos os métodos para um ponto Pareto fraco ótimo é obtido.Submitted by Ana Caroline Costa (ana_caroline212@hotmail.com) on 2019-03-28T18:36:51Z No. of bitstreams: 2 Tese - Lucas Vidal de Meireles - 2019.pdf: 1345051 bytes, checksum: 426759fdd43063c99bbba410a09a38b3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2019-03-29T13:49:52Z (GMT) No. of bitstreams: 2 Tese - Lucas Vidal de Meireles - 2019.pdf: 1345051 bytes, checksum: 426759fdd43063c99bbba410a09a38b3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2019-03-29T13:49:52Z (GMT). No. of bitstreams: 2 Tese - Lucas Vidal de Meireles - 2019.pdf: 1345051 bytes, checksum: 426759fdd43063c99bbba410a09a38b3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2019-02-26Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfengUniversidade 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/openAccessOtimização multiobjetivoCondições de otimalidadeMétodo do ponto proximalSolução aproximadaVariedades riemannianaMultiobjective optimizationOptimality conditionsProximal point methodApproximate solutionRiemannian manifoldsCIENCIAS EXATAS E DA TERRA::MATEMATICAProximal point methods for multiobjective optimization in riemannian manifoldsMétodo do ponto proximal para otimização multiobjetivo 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 Proximal point methods for multiobjective optimization in riemannian manifolds
dc.title.alternative.por.fl_str_mv Método do ponto proximal para otimização multiobjetivo em variedades riemannianas
title Proximal point methods for multiobjective optimization in riemannian manifolds
spellingShingle Proximal point methods for multiobjective optimization in riemannian manifolds
Meireles, Lucas Vidal de
Otimização multiobjetivo
Condições de otimalidade
Método do ponto proximal
Solução aproximada
Variedades riemanniana
Multiobjective optimization
Optimality conditions
Proximal point method
Approximate solution
Riemannian manifolds
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Proximal point methods for multiobjective optimization in riemannian manifolds
title_full Proximal point methods for multiobjective optimization in riemannian manifolds
title_fullStr Proximal point methods for multiobjective optimization in riemannian manifolds
title_full_unstemmed Proximal point methods for multiobjective optimization in riemannian manifolds
title_sort Proximal point methods for multiobjective optimization in riemannian manifolds
author Meireles, Lucas Vidal de
author_facet Meireles, Lucas Vidal de
author_role author
dc.contributor.advisor1.fl_str_mv Bento, Glaydston de Carvalho
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/1089906772427394
dc.contributor.referee1.fl_str_mv Bento, Glaydston de Carvalho
dc.contributor.referee2.fl_str_mv Oliveira, Paulo Roberto
dc.contributor.referee3.fl_str_mv Santos, Paulo Sérgio Marques dos
dc.contributor.referee4.fl_str_mv Cruz Neto, João Xavier da
dc.contributor.referee5.fl_str_mv Ferreira, Orizon Pereira
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/9108358595172188
dc.contributor.author.fl_str_mv Meireles, Lucas Vidal de
contributor_str_mv Bento, Glaydston de Carvalho
Bento, Glaydston de Carvalho
Oliveira, Paulo Roberto
Santos, Paulo Sérgio Marques dos
Cruz Neto, João Xavier da
Ferreira, Orizon Pereira
dc.subject.por.fl_str_mv Otimização multiobjetivo
Condições de otimalidade
Método do ponto proximal
Solução aproximada
Variedades riemanniana
topic Otimização multiobjetivo
Condições de otimalidade
Método do ponto proximal
Solução aproximada
Variedades riemanniana
Multiobjective optimization
Optimality conditions
Proximal point method
Approximate solution
Riemannian manifolds
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Multiobjective optimization
Optimality conditions
Proximal point method
Approximate solution
Riemannian manifolds
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this work, two different proximal-type methods are investigated in the Riemannian context, namely, an exact and an inexact version. Two strategies were used to analyze these methods. For the exact version, we used a direct approach by investigating the regularized problem, not considering any convexity assumption over the constraint sets, that determine the vectorial improvement steps, which replaces the classical approach via scalarization. To study the inexact version, a definition of the approximate Pareto efficient solution is introduced. For the convex case on Hadamard manifolds, full convergence of both methods to a weak Pareto optimal point is obtained.
publishDate 2019
dc.date.accessioned.fl_str_mv 2019-03-29T13:49:52Z
dc.date.issued.fl_str_mv 2019-02-26
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
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dc.identifier.citation.fl_str_mv MEIRELES, L. V. Proximal point methods for multiobjective optimization in riemannian manifolds. 2019. 49 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/9410
dc.identifier.dark.fl_str_mv ark:/38995/0013000003bk3
identifier_str_mv MEIRELES, L. V. Proximal point methods for multiobjective optimization in riemannian manifolds. 2019. 49 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.
ark:/38995/0013000003bk3
url http://repositorio.bc.ufg.br/tede/handle/tede/9410
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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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