A projected Weiszfeld algorithm for the box-constrained Weber location problem

Autores
Pilotta, Elvio Angel; Torres, German Ariel
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Weber problem consists of finding a point that minimizes the weighted sum of distances from m points that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed-point iteration. In this work we generalize the Weber location problem considering box constraints. We propose a fixed-point iteration with projections on the constraints and demonstrate descending properties. It is also proved that the limit of the sequence generated by the method is a feasible point and satisfiesthe KKT optimality conditions. Numerical experiments are presented to validate the theoretical results.
Fil: Pilotta, Elvio Angel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Torres, German Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
WEBER PROBLEM
BOX- CONSTRAINTS
FIXED-POINT ITERATION
LOCATION PROBLEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/268546
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A projected Weiszfeld algorithm for the box-constrained Weber location problemPilotta, Elvio AngelTorres, German ArielWEBER PROBLEMBOX- CONSTRAINTSFIXED-POINT ITERATIONLOCATION PROBLEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The Weber problem consists of finding a point that minimizes the weighted sum of distances from m points that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed-point iteration. In this work we generalize the Weber location problem considering box constraints. We propose a fixed-point iteration with projections on the constraints and demonstrate descending properties. It is also proved that the limit of the sequence generated by the method is a feasible point and satisfiesthe KKT optimality conditions. Numerical experiments are presented to validate the theoretical results.Fil: Pilotta, Elvio Angel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Torres, German Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaElsevier Science Inc.2011-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/268546Pilotta, Elvio Angel; Torres, German Ariel; A projected Weiszfeld algorithm for the box-constrained Weber location problem; Elsevier Science Inc.; Applied Mathematics and Computation; 218; 6; 11-2011; 2932-29430096-3003CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2011.08.041info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:00:50Zoai:ri.conicet.gov.ar:11336/268546instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:00:50.523CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A projected Weiszfeld algorithm for the box-constrained Weber location problem
title A projected Weiszfeld algorithm for the box-constrained Weber location problem
spellingShingle A projected Weiszfeld algorithm for the box-constrained Weber location problem
Pilotta, Elvio Angel
WEBER PROBLEM
BOX- CONSTRAINTS
FIXED-POINT ITERATION
LOCATION PROBLEMS
title_short A projected Weiszfeld algorithm for the box-constrained Weber location problem
title_full A projected Weiszfeld algorithm for the box-constrained Weber location problem
title_fullStr A projected Weiszfeld algorithm for the box-constrained Weber location problem
title_full_unstemmed A projected Weiszfeld algorithm for the box-constrained Weber location problem
title_sort A projected Weiszfeld algorithm for the box-constrained Weber location problem
dc.creator.none.fl_str_mv Pilotta, Elvio Angel
Torres, German Ariel
author Pilotta, Elvio Angel
author_facet Pilotta, Elvio Angel
Torres, German Ariel
author_role author
author2 Torres, German Ariel
author2_role author
dc.subject.none.fl_str_mv WEBER PROBLEM
BOX- CONSTRAINTS
FIXED-POINT ITERATION
LOCATION PROBLEMS
topic WEBER PROBLEM
BOX- CONSTRAINTS
FIXED-POINT ITERATION
LOCATION PROBLEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Weber problem consists of finding a point that minimizes the weighted sum of distances from m points that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed-point iteration. In this work we generalize the Weber location problem considering box constraints. We propose a fixed-point iteration with projections on the constraints and demonstrate descending properties. It is also proved that the limit of the sequence generated by the method is a feasible point and satisfiesthe KKT optimality conditions. Numerical experiments are presented to validate the theoretical results.
Fil: Pilotta, Elvio Angel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Torres, German Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description The Weber problem consists of finding a point that minimizes the weighted sum of distances from m points that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed-point iteration. In this work we generalize the Weber location problem considering box constraints. We propose a fixed-point iteration with projections on the constraints and demonstrate descending properties. It is also proved that the limit of the sequence generated by the method is a feasible point and satisfiesthe KKT optimality conditions. Numerical experiments are presented to validate the theoretical results.
publishDate 2011
dc.date.none.fl_str_mv 2011-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/268546
Pilotta, Elvio Angel; Torres, German Ariel; A projected Weiszfeld algorithm for the box-constrained Weber location problem; Elsevier Science Inc.; Applied Mathematics and Computation; 218; 6; 11-2011; 2932-2943
0096-3003
CONICET Digital
CONICET
url http://hdl.handle.net/11336/268546
identifier_str_mv Pilotta, Elvio Angel; Torres, German Ariel; A projected Weiszfeld algorithm for the box-constrained Weber location problem; Elsevier Science Inc.; Applied Mathematics and Computation; 218; 6; 11-2011; 2932-2943
0096-3003
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2011.08.041
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc.
publisher.none.fl_str_mv Elsevier Science Inc.
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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