A global hybrid derivative-free method for high-dimensional systems of nonlinear equations

Detalhes bibliográficos
Autor(a) principal: Begiato, Rodolfo G.
Data de Publicação: 2020
Outros Autores: Custódio, Ana Luisa, Gomes-Ruggiero, Márcia A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/116219
Resumo: Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the projects PTDC/MAT-APL/28400/2017 and UID/MAT/00297/2019. Marcia A. Gomes-Ruggiero: Partially supported by PRONEX-Optimization; CNPq (Grants 306220/2009-1 and 309733/2013-8); FAPESP (Grants 2013/05475-7 and 2013/07375-0) and CAPES.
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spelling A global hybrid derivative-free method for high-dimensional systems of nonlinear equationsDerivative-free optimization methodsInexact NewtonNonlinear systems of equationsNonmonotone line searchSpectral residualControl and OptimizationComputational MathematicsApplied MathematicsFundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the projects PTDC/MAT-APL/28400/2017 and UID/MAT/00297/2019. Marcia A. Gomes-Ruggiero: Partially supported by PRONEX-Optimization; CNPq (Grants 306220/2009-1 and 309733/2013-8); FAPESP (Grants 2013/05475-7 and 2013/07375-0) and CAPES.This work concerns the numerical solution of high-dimensional systems of nonlinear equations, when derivatives are not available for use, but assuming that all functions defining the problem are continuously differentiable. A hybrid approach is taken, based on a derivative-free iterative method, organized in two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists on a matrix-free inexact Newton method that employs the Generalized Minimal Residual algorithm to solve the linear system that computes the search direction. This second phase will only take place if the first one fails to find a better point after a predefined number of reductions in the step size. In all stages, the criterion to accept a new point considers a nonmonotone decrease condition upon a merit function. Convergence results are established and the numerical performance is assessed through experiments in a set of problems collected from the literature. Both the theoretical and the experimental analysis support the feasibility of the proposed hybrid strategy.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNBegiato, Rodolfo G.Custódio, Ana LuisaGomes-Ruggiero, Márcia A.2021-04-26T22:55:03Z2020-01-012020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article20application/pdfhttp://hdl.handle.net/10362/116219eng0926-6003PURE: 15483455https://doi.org/10.1007/s10589-019-00149-yinfo: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:RCAAP2024-03-11T04:58:41Zoai:run.unl.pt:10362/116219Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:42:59.699158Repositório 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 global hybrid derivative-free method for high-dimensional systems of nonlinear equations
title A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
spellingShingle A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
Begiato, Rodolfo G.
Derivative-free optimization methods
Inexact Newton
Nonlinear systems of equations
Nonmonotone line search
Spectral residual
Control and Optimization
Computational Mathematics
Applied Mathematics
title_short A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
title_full A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
title_fullStr A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
title_full_unstemmed A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
title_sort A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
author Begiato, Rodolfo G.
author_facet Begiato, Rodolfo G.
Custódio, Ana Luisa
Gomes-Ruggiero, Márcia A.
author_role author
author2 Custódio, Ana Luisa
Gomes-Ruggiero, Márcia A.
author2_role author
author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Begiato, Rodolfo G.
Custódio, Ana Luisa
Gomes-Ruggiero, Márcia A.
dc.subject.por.fl_str_mv Derivative-free optimization methods
Inexact Newton
Nonlinear systems of equations
Nonmonotone line search
Spectral residual
Control and Optimization
Computational Mathematics
Applied Mathematics
topic Derivative-free optimization methods
Inexact Newton
Nonlinear systems of equations
Nonmonotone line search
Spectral residual
Control and Optimization
Computational Mathematics
Applied Mathematics
description Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the projects PTDC/MAT-APL/28400/2017 and UID/MAT/00297/2019. Marcia A. Gomes-Ruggiero: Partially supported by PRONEX-Optimization; CNPq (Grants 306220/2009-1 and 309733/2013-8); FAPESP (Grants 2013/05475-7 and 2013/07375-0) and CAPES.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-01
2020-01-01T00:00:00Z
2021-04-26T22:55:03Z
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/10362/116219
url http://hdl.handle.net/10362/116219
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0926-6003
PURE: 15483455
https://doi.org/10.1007/s10589-019-00149-y
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 20
application/pdf
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
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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
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