Properties of the delayed weighted gradient method
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Data de Publicação: | 2021 |
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Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/144737 |
Resumo: | Funding Information: Roberto Andreani was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). Marcos Raydan 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). Roberto Andreani would like to thank the Operations Research Group at CMA (Centro de Matemática e Aplicações), FCT, NOVA University of Lisbon, Portugal, for the hospitality during a two-week visit in December 2019. Funding Information: We would like to thank two anonymous referees for their comments and suggestions that helped us to improve the final version of this paper. Roberto Andreani was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). Marcos Raydan 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). Roberto Andreani would like to thank the Operations Research Group at CMA (Centro de Matemática e Aplicações), FCT, NOVA University of Lisbon, Portugal, for the hospitality during a two-week visit in December 2019. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. |
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Properties of the delayed weighted gradient methodConjugate gradient methodsFinite terminationGradient methodsKrylov subspace methodsSmoothing techniquesControl and OptimizationComputational MathematicsApplied MathematicsFunding Information: Roberto Andreani was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). Marcos Raydan 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). Roberto Andreani would like to thank the Operations Research Group at CMA (Centro de Matemática e Aplicações), FCT, NOVA University of Lisbon, Portugal, for the hospitality during a two-week visit in December 2019. Funding Information: We would like to thank two anonymous referees for their comments and suggestions that helped us to improve the final version of this paper. Roberto Andreani was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). Marcos Raydan 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). Roberto Andreani would like to thank the Operations Research Group at CMA (Centro de Matemática e Aplicações), FCT, NOVA University of Lisbon, Portugal, for the hospitality during a two-week visit in December 2019. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature.The delayed weighted gradient method, recently introduced in Oviedo-Leon (Comput Optim Appl 74:729–746, 2019), is a low-cost gradient-type method that exhibits a surprisingly and perhaps unexpected fast convergence behavior that competes favorably with the well-known conjugate gradient method for the minimization of convex quadratic functions. In this work, we establish several orthogonality properties that add understanding to the practical behavior of the method, including its finite termination. We show that if the n× n real Hessian matrix of the quadratic function has only p< n distinct eigenvalues, then the method terminates in p iterations. We also establish an optimality condition, concerning the gradient norm, that motivates the future use of this novel scheme when low precision is required for the minimization of non-quadratic functions.CMA - Centro de Matemática e AplicaçõesRUNAndreani, RobertoRaydan, Marcos2022-10-14T22:14:13Z2021-012021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article14application/pdfhttp://hdl.handle.net/10362/144737eng0926-6003PURE: 45487415https://doi.org/10.1007/s10589-020-00232-9info: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:RCAAP2024-03-11T05:24:36Zoai:run.unl.pt:10362/144737Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:51:43.671385Repositório 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 |
Properties of the delayed weighted gradient method |
title |
Properties of the delayed weighted gradient method |
spellingShingle |
Properties of the delayed weighted gradient method Andreani, Roberto Conjugate gradient methods Finite termination Gradient methods Krylov subspace methods Smoothing techniques Control and Optimization Computational Mathematics Applied Mathematics |
title_short |
Properties of the delayed weighted gradient method |
title_full |
Properties of the delayed weighted gradient method |
title_fullStr |
Properties of the delayed weighted gradient method |
title_full_unstemmed |
Properties of the delayed weighted gradient method |
title_sort |
Properties of the delayed weighted gradient method |
author |
Andreani, Roberto |
author_facet |
Andreani, Roberto Raydan, Marcos |
author_role |
author |
author2 |
Raydan, Marcos |
author2_role |
author |
dc.contributor.none.fl_str_mv |
CMA - Centro de Matemática e Aplicações RUN |
dc.contributor.author.fl_str_mv |
Andreani, Roberto Raydan, Marcos |
dc.subject.por.fl_str_mv |
Conjugate gradient methods Finite termination Gradient methods Krylov subspace methods Smoothing techniques Control and Optimization Computational Mathematics Applied Mathematics |
topic |
Conjugate gradient methods Finite termination Gradient methods Krylov subspace methods Smoothing techniques Control and Optimization Computational Mathematics Applied Mathematics |
description |
Funding Information: Roberto Andreani was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). Marcos Raydan 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). Roberto Andreani would like to thank the Operations Research Group at CMA (Centro de Matemática e Aplicações), FCT, NOVA University of Lisbon, Portugal, for the hospitality during a two-week visit in December 2019. Funding Information: We would like to thank two anonymous referees for their comments and suggestions that helped us to improve the final version of this paper. Roberto Andreani was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). Marcos Raydan 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). Roberto Andreani would like to thank the Operations Research Group at CMA (Centro de Matemática e Aplicações), FCT, NOVA University of Lisbon, Portugal, for the hospitality during a two-week visit in December 2019. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01 2021-01-01T00:00:00Z 2022-10-14T22:14:13Z |
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/10362/144737 |
url |
http://hdl.handle.net/10362/144737 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0926-6003 PURE: 45487415 https://doi.org/10.1007/s10589-020-00232-9 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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14 application/pdf |
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reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799138109904912384 |