Two derivative-free methods for solving underdetermined nonlinear systems of equations

Autores
Echebest, Nélida Ester; Schuverdt, María Laura; Vignau, Raúl Pedro
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
derivative-free line search
global convergence
quasi-Newton method
spectral step length
underdetermined nonlinear systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc/3.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/40172

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network_name_str SEDICI (UNLP)
spelling Two derivative-free methods for solving underdetermined nonlinear systems of equationsEchebest, Nélida EsterSchuverdt, María LauraVignau, Raúl PedroCiencias ExactasMatemáticaderivative-free line searchglobal convergencequasi-Newton methodspectral step lengthunderdetermined nonlinear systemsIn this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.Facultad de Ciencias Exactas2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf217-245http://sedici.unlp.edu.ar/handle/10915/40172enginfo:eu-repo/semantics/altIdentifier/url/http://www.scielo.br/pdf/cam/v30n1/11.pdfinfo:eu-repo/semantics/altIdentifier/issn/0101-8205info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/3.0/Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T10:57:04Zoai:sedici.unlp.edu.ar:10915/40172Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 10:57:04.304SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Two derivative-free methods for solving underdetermined nonlinear systems of equations
title Two derivative-free methods for solving underdetermined nonlinear systems of equations
spellingShingle Two derivative-free methods for solving underdetermined nonlinear systems of equations
Echebest, Nélida Ester
Ciencias Exactas
Matemática
derivative-free line search
global convergence
quasi-Newton method
spectral step length
underdetermined nonlinear systems
title_short Two derivative-free methods for solving underdetermined nonlinear systems of equations
title_full Two derivative-free methods for solving underdetermined nonlinear systems of equations
title_fullStr Two derivative-free methods for solving underdetermined nonlinear systems of equations
title_full_unstemmed Two derivative-free methods for solving underdetermined nonlinear systems of equations
title_sort Two derivative-free methods for solving underdetermined nonlinear systems of equations
dc.creator.none.fl_str_mv Echebest, Nélida Ester
Schuverdt, María Laura
Vignau, Raúl Pedro
author Echebest, Nélida Ester
author_facet Echebest, Nélida Ester
Schuverdt, María Laura
Vignau, Raúl Pedro
author_role author
author2 Schuverdt, María Laura
Vignau, Raúl Pedro
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
derivative-free line search
global convergence
quasi-Newton method
spectral step length
underdetermined nonlinear systems
topic Ciencias Exactas
Matemática
derivative-free line search
global convergence
quasi-Newton method
spectral step length
underdetermined nonlinear systems
dc.description.none.fl_txt_mv In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.
Facultad de Ciencias Exactas
description In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/40172
url http://sedici.unlp.edu.ar/handle/10915/40172
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.scielo.br/pdf/cam/v30n1/11.pdf
info:eu-repo/semantics/altIdentifier/issn/0101-8205
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc/3.0/
Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc/3.0/
Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)
dc.format.none.fl_str_mv application/pdf
217-245
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instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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