Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case
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/10316/44582 https://doi.org/10.1137/151005683 |
Resumo: | Trust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proven to generate a sequence of iterates converging to stationarity independently of the starting point. Most of such an analysis is carried out in the smooth case, and, moreover, little is known about the complexity or global rate of these methods. In this paper, we start by analyzing the worst case complexity of general trust-region derivative-free methods for smooth functions. For the nonsmooth case, we propose a smoothing approach, for which we prove global convergence and bound the worst case complexity effort. For the special case of nonsmooth functions that result from the composition of smooth and nonsmooth/convex components, we show how to improve the existing results of the literature and make them applicable to the general methodology. |
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7160 |
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Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth CaseTrust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proven to generate a sequence of iterates converging to stationarity independently of the starting point. Most of such an analysis is carried out in the smooth case, and, moreover, little is known about the complexity or global rate of these methods. In this paper, we start by analyzing the worst case complexity of general trust-region derivative-free methods for smooth functions. For the nonsmooth case, we propose a smoothing approach, for which we prove global convergence and bound the worst case complexity effort. For the special case of nonsmooth functions that result from the composition of smooth and nonsmooth/convex components, we show how to improve the existing results of the literature and make them applicable to the general methodology.Society for Industrial and Applied Mathematics (SIAM)2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44582http://hdl.handle.net/10316/44582https://doi.org/10.1137/151005683https://doi.org/10.1137/151005683enghttps://doi.org/10.1137/151005683Garmanjani, RohollahJúdice, DiogoVicente, 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:RCAAP2021-06-29T10:03:20Zoai:estudogeral.uc.pt:10316/44582Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:24.801527Repositório 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 |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
title |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
spellingShingle |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case Garmanjani, Rohollah |
title_short |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
title_full |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
title_fullStr |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
title_full_unstemmed |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
title_sort |
Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case |
author |
Garmanjani, Rohollah |
author_facet |
Garmanjani, Rohollah Júdice, Diogo Vicente, Luís Nunes |
author_role |
author |
author2 |
Júdice, Diogo Vicente, Luís Nunes |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Garmanjani, Rohollah Júdice, Diogo Vicente, Luís Nunes |
description |
Trust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proven to generate a sequence of iterates converging to stationarity independently of the starting point. Most of such an analysis is carried out in the smooth case, and, moreover, little is known about the complexity or global rate of these methods. In this paper, we start by analyzing the worst case complexity of general trust-region derivative-free methods for smooth functions. For the nonsmooth case, we propose a smoothing approach, for which we prove global convergence and bound the worst case complexity effort. For the special case of nonsmooth functions that result from the composition of smooth and nonsmooth/convex components, we show how to improve the existing results of the literature and make them applicable to the general methodology. |
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/10316/44582 http://hdl.handle.net/10316/44582 https://doi.org/10.1137/151005683 https://doi.org/10.1137/151005683 |
url |
http://hdl.handle.net/10316/44582 https://doi.org/10.1137/151005683 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1137/151005683 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics (SIAM) |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics (SIAM) |
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 |
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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 |
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1799133821133651968 |