A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization

Detalhes bibliográficos
Autor(a) principal: Oviedo, Harry
Data de Publicação: 2022
Outros Autores: Andreani, Roberto, Raydan, Marcos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/161565
Resumo: Funding Information: The first author was financially supported by FGV (Fundação Getulio Vargas) through the excellence post–doctoral fellowship program. The second author was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). The third author was financially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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spelling A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimizationConjugate gradient methodsGradient methodsMoreau envelopeStrictly convex quadraticsUnconstrained optimizationApplied MathematicsFunding Information: The first author was financially supported by FGV (Fundação Getulio Vargas) through the excellence post–doctoral fellowship program. The second author was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). The third author was financially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.We introduce a family of weighted conjugate-gradient-type methods, for strictly convex quadratic functions, whose parameters are determined by a minimization model based on a convex combination of the objective function and its gradient norm. This family includes the classical linear conjugate gradient method and the recently published delayed weighted gradient method as the extreme cases of the convex combination. The inner cases produce a merit function that offers a compromise between function-value reduction and stationarity which is convenient for real applications. We show that each one of the infinitely many members of the family exhibits q-linear convergence to the unique solution. Moreover, each one of them enjoys finite termination and an optimality property related to the combined merit function. In particular, we prove that if the n × n Hessian of the quadratic function has p < n different eigenvalues, then each member of the family obtains the unique global minimizer in exactly p iterations. Numerical results are presented that demonstrate that the proposed family is promising and exhibits a fast convergence behavior which motivates the use of preconditioning strategies, as well as its extension to the numerical solution of general unconstrained optimization problems.CMA - Centro de Matemática e AplicaçõesRUNOviedo, HarryAndreani, RobertoRaydan, Marcos2023-12-22T01:37:36Z2022-072022-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article28application/pdfhttp://hdl.handle.net/10362/161565eng1017-1398PURE: 76352143https://doi.org/10.1007/s11075-021-01228-0info: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:RCAAP2024-03-11T05:44:29Zoai:run.unl.pt:10362/161565Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:58:35.509802Repositório 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 family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
title A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
spellingShingle A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
Oviedo, Harry
Conjugate gradient methods
Gradient methods
Moreau envelope
Strictly convex quadratics
Unconstrained optimization
Applied Mathematics
title_short A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
title_full A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
title_fullStr A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
title_full_unstemmed A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
title_sort A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization
author Oviedo, Harry
author_facet Oviedo, Harry
Andreani, Roberto
Raydan, Marcos
author_role author
author2 Andreani, Roberto
Raydan, Marcos
author2_role author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Oviedo, Harry
Andreani, Roberto
Raydan, Marcos
dc.subject.por.fl_str_mv Conjugate gradient methods
Gradient methods
Moreau envelope
Strictly convex quadratics
Unconstrained optimization
Applied Mathematics
topic Conjugate gradient methods
Gradient methods
Moreau envelope
Strictly convex quadratics
Unconstrained optimization
Applied Mathematics
description Funding Information: The first author was financially supported by FGV (Fundação Getulio Vargas) through the excellence post–doctoral fellowship program. The second author was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). The third author was financially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
publishDate 2022
dc.date.none.fl_str_mv 2022-07
2022-07-01T00:00:00Z
2023-12-22T01:37:36Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/161565
url http://hdl.handle.net/10362/161565
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1017-1398
PURE: 76352143
https://doi.org/10.1007/s11075-021-01228-0
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 28
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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