Direct search based on probabilistic feasible descent for bound and linearly constrained problems
Autor(a) principal: | |
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Data de Publicação: | 2019 |
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/10316/89442 https://doi.org/10.1007/s10589-019-00062-4 |
Resumo: | Direct search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region, and typically consist of positive generators of approximate tangent cones (which then renders the corresponding methods globally convergent in the linearly constrained case). One knows however from the unconstrained case that randomly generating the polling directions leads to better complexity bounds as well as to gains in numerical efficiency, and it becomes then natural to consider random generation also in the presence of constraints. In this paper, we study a class of direct-search methods based on sufficient decrease for solving smooth linearly constrained problems where the polling directions are randomly generated (in approximate tangent cones). The random polling directions must satisfy probabilistic feasible descent, a concept which reduces to probabilistic descent in the absence of constraints. Such a property is instrumental in establishing almost-sure global convergence and worst-case complexity bounds with overwhelming probability. Numerical results show that the randomization of the polling directions can be beneficial over standard approaches with deterministic guarantees, as it is suggested by the respective worst-case complexity bounds. |
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Direct search based on probabilistic feasible descent for bound and linearly constrained problemsDerivative-free optimization; Direct-search methods; Bound constraints; Linear constraints; Feasible descent; Probabilistic feasible descent; Worst-case complexityDirect search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region, and typically consist of positive generators of approximate tangent cones (which then renders the corresponding methods globally convergent in the linearly constrained case). One knows however from the unconstrained case that randomly generating the polling directions leads to better complexity bounds as well as to gains in numerical efficiency, and it becomes then natural to consider random generation also in the presence of constraints. In this paper, we study a class of direct-search methods based on sufficient decrease for solving smooth linearly constrained problems where the polling directions are randomly generated (in approximate tangent cones). The random polling directions must satisfy probabilistic feasible descent, a concept which reduces to probabilistic descent in the absence of constraints. Such a property is instrumental in establishing almost-sure global convergence and worst-case complexity bounds with overwhelming probability. Numerical results show that the randomization of the polling directions can be beneficial over standard approaches with deterministic guarantees, as it is suggested by the respective worst-case complexity bounds.Springer Verlag2019-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/89442http://hdl.handle.net/10316/89442https://doi.org/10.1007/s10589-019-00062-4enghttps://link.springer.com/article/10.1007/s10589-019-00062-4Gratton, SergeRoyer, Clément WVicente, Luís NunesZhang, Zaikuninfo: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:RCAAP2022-05-25T03:06:09Zoai:estudogeral.uc.pt:10316/89442Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:09:45.338242Repositório 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 |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
title |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
spellingShingle |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems Gratton, Serge Derivative-free optimization; Direct-search methods; Bound constraints; Linear constraints; Feasible descent; Probabilistic feasible descent; Worst-case complexity |
title_short |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
title_full |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
title_fullStr |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
title_full_unstemmed |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
title_sort |
Direct search based on probabilistic feasible descent for bound and linearly constrained problems |
author |
Gratton, Serge |
author_facet |
Gratton, Serge Royer, Clément W Vicente, Luís Nunes Zhang, Zaikun |
author_role |
author |
author2 |
Royer, Clément W Vicente, Luís Nunes Zhang, Zaikun |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Gratton, Serge Royer, Clément W Vicente, Luís Nunes Zhang, Zaikun |
dc.subject.por.fl_str_mv |
Derivative-free optimization; Direct-search methods; Bound constraints; Linear constraints; Feasible descent; Probabilistic feasible descent; Worst-case complexity |
topic |
Derivative-free optimization; Direct-search methods; Bound constraints; Linear constraints; Feasible descent; Probabilistic feasible descent; Worst-case complexity |
description |
Direct search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region, and typically consist of positive generators of approximate tangent cones (which then renders the corresponding methods globally convergent in the linearly constrained case). One knows however from the unconstrained case that randomly generating the polling directions leads to better complexity bounds as well as to gains in numerical efficiency, and it becomes then natural to consider random generation also in the presence of constraints. In this paper, we study a class of direct-search methods based on sufficient decrease for solving smooth linearly constrained problems where the polling directions are randomly generated (in approximate tangent cones). The random polling directions must satisfy probabilistic feasible descent, a concept which reduces to probabilistic descent in the absence of constraints. Such a property is instrumental in establishing almost-sure global convergence and worst-case complexity bounds with overwhelming probability. Numerical results show that the randomization of the polling directions can be beneficial over standard approaches with deterministic guarantees, as it is suggested by the respective worst-case complexity bounds. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-01 |
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/10316/89442 http://hdl.handle.net/10316/89442 https://doi.org/10.1007/s10589-019-00062-4 |
url |
http://hdl.handle.net/10316/89442 https://doi.org/10.1007/s10589-019-00062-4 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://link.springer.com/article/10.1007/s10589-019-00062-4 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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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1799133992886206464 |