Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization

Detalhes bibliográficos
Autor(a) principal: Custódio, Ana Luísa
Data de Publicação: 2021
Outros Autores: Diouane, Youssef, Garmanjani, Rohollah, Riccietti, Elisa
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/117466
Resumo: Funding support for Ana Luisa Custodio and Rohollah Garmanjani was provided by national funds through FCT-FundacAo para a Ciencia e a Tecnologia I. P., under the scope of Projects PTDC/MAT-APL/28400/2017 and UIDB/00297/2020. Support for Elisa Riccietti was provided by TOTAL E&P.
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spelling Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective OptimizationDerivative-free optimization methodsDirectional direct-searchMultiobjective unconstrained optimizationNonconvex smooth optimizationWorst-case complexityControl and OptimizationManagement Science and Operations ResearchApplied MathematicsFunding support for Ana Luisa Custodio and Rohollah Garmanjani was provided by national funds through FCT-FundacAo para a Ciencia e a Tecnologia I. P., under the scope of Projects PTDC/MAT-APL/28400/2017 and UIDB/00297/2020. Support for Elisa Riccietti was provided by TOTAL E&P.Direct Multisearch is a well-established class of algorithms, suited for multiobjective derivative-free optimization. In this work, we analyze the worst-case complexity of this class of methods in its most general formulation for unconstrained optimization. Considering nonconvex smooth functions, we show that to drive a given criticality measure below a specific positive threshold, Direct Multisearch takes at most a number of iterations proportional to the square of the inverse of the threshold, raised to the number of components of the objective function. This number is also proportional to the size of the set of linked sequences between the first unsuccessful iteration and the iteration immediately before the one where the criticality condition is satisfied. We then focus on a particular instance of Direct Multisearch, which considers a more strict criterion for accepting new nondominated points. In this case, we can establish a better worst-case complexity bound, simply proportional to the square of the inverse of the threshold, for driving the same criticality measure below the considered threshold.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNCustódio, Ana LuísaDiouane, YoussefGarmanjani, RohollahRiccietti, Elisa2022-03-31T00:31:40Z2021-012021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/117466eng0022-3239PURE: 26922201https://doi.org/10.1007/s10957-020-01781-zinfo: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:RCAAP2024-03-11T05:00:32Zoai:run.unl.pt:10362/117466Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:43:36.882770Repositório 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 Bounds of Directional Direct-Search Methods for Multiobjective Optimization
title Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
spellingShingle Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
Custódio, Ana Luísa
Derivative-free optimization methods
Directional direct-search
Multiobjective unconstrained optimization
Nonconvex smooth optimization
Worst-case complexity
Control and Optimization
Management Science and Operations Research
Applied Mathematics
title_short Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
title_full Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
title_fullStr Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
title_full_unstemmed Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
title_sort Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization
author Custódio, Ana Luísa
author_facet Custódio, Ana Luísa
Diouane, Youssef
Garmanjani, Rohollah
Riccietti, Elisa
author_role author
author2 Diouane, Youssef
Garmanjani, Rohollah
Riccietti, Elisa
author2_role author
author
author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Custódio, Ana Luísa
Diouane, Youssef
Garmanjani, Rohollah
Riccietti, Elisa
dc.subject.por.fl_str_mv Derivative-free optimization methods
Directional direct-search
Multiobjective unconstrained optimization
Nonconvex smooth optimization
Worst-case complexity
Control and Optimization
Management Science and Operations Research
Applied Mathematics
topic Derivative-free optimization methods
Directional direct-search
Multiobjective unconstrained optimization
Nonconvex smooth optimization
Worst-case complexity
Control and Optimization
Management Science and Operations Research
Applied Mathematics
description Funding support for Ana Luisa Custodio and Rohollah Garmanjani was provided by national funds through FCT-FundacAo para a Ciencia e a Tecnologia I. P., under the scope of Projects PTDC/MAT-APL/28400/2017 and UIDB/00297/2020. Support for Elisa Riccietti was provided by TOTAL E&P.
publishDate 2021
dc.date.none.fl_str_mv 2021-01
2021-01-01T00:00:00Z
2022-03-31T00:31:40Z
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/10362/117466
url http://hdl.handle.net/10362/117466
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-3239
PURE: 26922201
https://doi.org/10.1007/s10957-020-01781-z
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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
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