A SURVEY ON MULTIOBJECTIVE DESCENT METHODS

Detalhes bibliográficos
Autor(a) principal: Fukuda,Ellen H.
Data de Publicação: 2014
Outros Autores: Drummond,Luis Mauricio Graña
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300585
Resumo: We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic
id SOBRAPO-1_6144b7da0d140dc6bdd7c5b7ed3543f5
oai_identifier_str oai:scielo:S0101-74382014000300585
network_acronym_str SOBRAPO-1
network_name_str Pesquisa operacional (Online)
repository_id_str
spelling A SURVEY ON MULTIOBJECTIVE DESCENT METHODSmultiobjective optimizationNewton methodnonlinear optimizationprojected gradient methodsteepest descent methodWe present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadraticSociedade Brasileira de Pesquisa Operacional2014-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300585Pesquisa Operacional v.34 n.3 2014reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/0101-7438.2014.034.03.0585info:eu-repo/semantics/openAccessFukuda,Ellen H.Drummond,Luis Mauricio Grañaeng2014-11-12T00:00:00Zoai:scielo:S0101-74382014000300585Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2014-11-12T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
title A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
spellingShingle A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
Fukuda,Ellen H.
multiobjective optimization
Newton method
nonlinear optimization
projected gradient method
steepest descent method
title_short A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
title_full A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
title_fullStr A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
title_full_unstemmed A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
title_sort A SURVEY ON MULTIOBJECTIVE DESCENT METHODS
author Fukuda,Ellen H.
author_facet Fukuda,Ellen H.
Drummond,Luis Mauricio Graña
author_role author
author2 Drummond,Luis Mauricio Graña
author2_role author
dc.contributor.author.fl_str_mv Fukuda,Ellen H.
Drummond,Luis Mauricio Graña
dc.subject.por.fl_str_mv multiobjective optimization
Newton method
nonlinear optimization
projected gradient method
steepest descent method
topic multiobjective optimization
Newton method
nonlinear optimization
projected gradient method
steepest descent method
description We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic
publishDate 2014
dc.date.none.fl_str_mv 2014-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300585
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382014000300585
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0101-7438.2014.034.03.0585
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.34 n.3 2014
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
_version_ 1750318017768587264

Registros relacionados