Properties of the delayed weighted gradient method

Detalhes bibliográficos
Autor(a) principal: Andreani, Roberto
Data de Publicação: 2021
Outros Autores: 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/10362/144737
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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spelling 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
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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
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eu_rights_str_mv openAccess
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