Global convergence of general derivative-free trust-region algorithms to first and second order critical points

Detalhes bibliográficos
Autor(a) principal: Conn, Andrew R.
Data de Publicação: 2006
Outros Autores: Scheinberg, Katya, Vicente, Luís Nunes
Tipo de documento: Outros
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: https://hdl.handle.net/10316/11325
Resumo: In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apart from that, the analysis is independent of the sampling techniques. A number of new issues are addressed, including global convergence when acceptance of iterates is based on simple decrease of the objective function, trust-region radius maintenance at the criticality step, and global convergence for second-order critical points.
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spelling Global convergence of general derivative-free trust-region algorithms to first and second order critical pointsTrust-region methodsDerivative-free optimizationNonlinear optimizationGlobal convergenceIn this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apart from that, the analysis is independent of the sampling techniques. A number of new issues are addressed, including global convergence when acceptance of iterates is based on simple decrease of the objective function, trust-region radius maintenance at the criticality step, and global convergence for second-order critical points.Centro de Matemática da Universidade de Coimbra; FCT under grant POCI/59442/MAT/2004Centro de Matemática da Universidade de Coimbra2006info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/otherhttps://hdl.handle.net/10316/11325https://hdl.handle.net/10316/11325engPré-Publicações DMUC. 06-49 (2006)Conn, Andrew R.Scheinberg, KatyaVicente, Luís Nunesinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2020-05-25T13:12:05Zoai:estudogeral.uc.pt:10316/11325Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T05:23:22.629059Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Global convergence of general derivative-free trust-region algorithms to first and second order critical points
title Global convergence of general derivative-free trust-region algorithms to first and second order critical points
spellingShingle Global convergence of general derivative-free trust-region algorithms to first and second order critical points
Conn, Andrew R.
Trust-region methods
Derivative-free optimization
Nonlinear optimization
Global convergence
title_short Global convergence of general derivative-free trust-region algorithms to first and second order critical points
title_full Global convergence of general derivative-free trust-region algorithms to first and second order critical points
title_fullStr Global convergence of general derivative-free trust-region algorithms to first and second order critical points
title_full_unstemmed Global convergence of general derivative-free trust-region algorithms to first and second order critical points
title_sort Global convergence of general derivative-free trust-region algorithms to first and second order critical points
author Conn, Andrew R.
author_facet Conn, Andrew R.
Scheinberg, Katya
Vicente, Luís Nunes
author_role author
author2 Scheinberg, Katya
Vicente, Luís Nunes
author2_role author
author
dc.contributor.author.fl_str_mv Conn, Andrew R.
Scheinberg, Katya
Vicente, Luís Nunes
dc.subject.por.fl_str_mv Trust-region methods
Derivative-free optimization
Nonlinear optimization
Global convergence
topic Trust-region methods
Derivative-free optimization
Nonlinear optimization
Global convergence
description In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apart from that, the analysis is independent of the sampling techniques. A number of new issues are addressed, including global convergence when acceptance of iterates is based on simple decrease of the objective function, trust-region radius maintenance at the criticality step, and global convergence for second-order critical points.
publishDate 2006
dc.date.none.fl_str_mv 2006
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/other
format other
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/10316/11325
https://hdl.handle.net/10316/11325
url https://hdl.handle.net/10316/11325
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Pré-Publicações DMUC. 06-49 (2006)
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Centro de Matemática da Universidade de Coimbra
publisher.none.fl_str_mv Centro de Matemática da Universidade de Coimbra
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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