Worst case complexity of direct search under convexity
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10316/45246 https://doi.org/10.1007/s10107-014-0847-0 |
Resumo: | In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is at most proportional to the inverse of the threshold. It will be also shown that the absolute error in the function values decay at a sublinear rate proportional to the inverse of the iteration counter. In addition, we prove that the sequence of absolute errors of function values and iterates converges r-linearly in the strongly convex case. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Worst case complexity of direct search under convexityIn this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is at most proportional to the inverse of the threshold. It will be also shown that the absolute error in the function values decay at a sublinear rate proportional to the inverse of the iteration counter. In addition, we prove that the sequence of absolute errors of function values and iterates converges r-linearly in the strongly convex case.Springer Berlin Heidelberg2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/45246http://hdl.handle.net/10316/45246https://doi.org/10.1007/s10107-014-0847-0https://doi.org/10.1007/s10107-014-0847-0enghttps://doi.org/10.1007/s10107-014-0847-0Dodangeh, MahdiVicente, Luís Nunesinfo: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:RCAAP2021-06-29T10:02:52Zoai:estudogeral.uc.pt:10316/45246Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:21.806582Repositório 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 |
Worst case complexity of direct search under convexity |
title |
Worst case complexity of direct search under convexity |
spellingShingle |
Worst case complexity of direct search under convexity Dodangeh, Mahdi |
title_short |
Worst case complexity of direct search under convexity |
title_full |
Worst case complexity of direct search under convexity |
title_fullStr |
Worst case complexity of direct search under convexity |
title_full_unstemmed |
Worst case complexity of direct search under convexity |
title_sort |
Worst case complexity of direct search under convexity |
author |
Dodangeh, Mahdi |
author_facet |
Dodangeh, Mahdi Vicente, Luís Nunes |
author_role |
author |
author2 |
Vicente, Luís Nunes |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Dodangeh, Mahdi Vicente, Luís Nunes |
description |
In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is at most proportional to the inverse of the threshold. It will be also shown that the absolute error in the function values decay at a sublinear rate proportional to the inverse of the iteration counter. In addition, we prove that the sequence of absolute errors of function values and iterates converges r-linearly in the strongly convex case. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 |
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/10316/45246 http://hdl.handle.net/10316/45246 https://doi.org/10.1007/s10107-014-0847-0 https://doi.org/10.1007/s10107-014-0847-0 |
url |
http://hdl.handle.net/10316/45246 https://doi.org/10.1007/s10107-014-0847-0 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1007/s10107-014-0847-0 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer Berlin Heidelberg |
publisher.none.fl_str_mv |
Springer Berlin Heidelberg |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
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 |
repository.mail.fl_str_mv |
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1799133820688007168 |