A Merit Function Approach for Direct Search
Autor(a) principal: | |
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Data de Publicação: | 2014 |
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/10316/45560 https://doi.org/10.1137/130917661 |
Resumo: | In this paper it is proposed to equip direct-search methods with a general procedure to minimize an objective function, possibly nonsmooth, without using derivatives and subject to constraints on the variables. One aims at considering constraints, most likely nonlinear or nonsmooth, for which the derivatives of the corresponding functions are also unavailable. The novelty of this contribution relies mostly on how relaxable constraints are handled. Such constraints, which can be relaxed during the course of the optimization, are taken care of by a merit function and, if necessary, by a restoration procedure. Constraints that are unrelaxable, when present, are treated by an extreme barrier approach. One is able to show that the resulting merit function direct-search algorithm exhibits global convergence properties for first-order stationary constraints. As in the progressive barrier method [C. Audet and J. E. Dennis Jr., SIAM J. Optim., 20 (2009), pp. 445--472], we provide a mechanism to indicate the transfer of constraints from the relaxable set to the unrelaxable one. |
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A Merit Function Approach for Direct SearchIn this paper it is proposed to equip direct-search methods with a general procedure to minimize an objective function, possibly nonsmooth, without using derivatives and subject to constraints on the variables. One aims at considering constraints, most likely nonlinear or nonsmooth, for which the derivatives of the corresponding functions are also unavailable. The novelty of this contribution relies mostly on how relaxable constraints are handled. Such constraints, which can be relaxed during the course of the optimization, are taken care of by a merit function and, if necessary, by a restoration procedure. Constraints that are unrelaxable, when present, are treated by an extreme barrier approach. One is able to show that the resulting merit function direct-search algorithm exhibits global convergence properties for first-order stationary constraints. As in the progressive barrier method [C. Audet and J. E. Dennis Jr., SIAM J. Optim., 20 (2009), pp. 445--472], we provide a mechanism to indicate the transfer of constraints from the relaxable set to the unrelaxable one.Society for Industrial and Applied Mathematics (SIAM)2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/45560http://hdl.handle.net/10316/45560https://doi.org/10.1137/130917661enghttp://epubs.siam.org/doi/abs/10.1137/130917661Gratton, SergeVicente, 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:RCAAP2019-06-01T18:35:07Zoai:estudogeral.uc.pt:10316/45560Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:25.376453Repositório 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 |
A Merit Function Approach for Direct Search |
title |
A Merit Function Approach for Direct Search |
spellingShingle |
A Merit Function Approach for Direct Search Gratton, Serge |
title_short |
A Merit Function Approach for Direct Search |
title_full |
A Merit Function Approach for Direct Search |
title_fullStr |
A Merit Function Approach for Direct Search |
title_full_unstemmed |
A Merit Function Approach for Direct Search |
title_sort |
A Merit Function Approach for Direct Search |
author |
Gratton, Serge |
author_facet |
Gratton, Serge Vicente, Luís Nunes |
author_role |
author |
author2 |
Vicente, Luís Nunes |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Gratton, Serge Vicente, Luís Nunes |
description |
In this paper it is proposed to equip direct-search methods with a general procedure to minimize an objective function, possibly nonsmooth, without using derivatives and subject to constraints on the variables. One aims at considering constraints, most likely nonlinear or nonsmooth, for which the derivatives of the corresponding functions are also unavailable. The novelty of this contribution relies mostly on how relaxable constraints are handled. Such constraints, which can be relaxed during the course of the optimization, are taken care of by a merit function and, if necessary, by a restoration procedure. Constraints that are unrelaxable, when present, are treated by an extreme barrier approach. One is able to show that the resulting merit function direct-search algorithm exhibits global convergence properties for first-order stationary constraints. As in the progressive barrier method [C. Audet and J. E. Dennis Jr., SIAM J. Optim., 20 (2009), pp. 445--472], we provide a mechanism to indicate the transfer of constraints from the relaxable set to the unrelaxable one. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014 |
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/10316/45560 http://hdl.handle.net/10316/45560 https://doi.org/10.1137/130917661 |
url |
http://hdl.handle.net/10316/45560 https://doi.org/10.1137/130917661 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
http://epubs.siam.org/doi/abs/10.1137/130917661 |
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 |
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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1799133821150429184 |