A new interior-point approach for large separable convex quadratic two-stage stochastic problems

Two-stage stochastic models give rise to very large optimization problems. Several approaches havebeen devised for efficiently solving them, including interior-point methods (IPMs). However, usingIPMs, the linking columns associated to first-stage decisions cause excessive fill-in for the solutionof...

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Autores: Castro Pérez, Jordi|||0000-0003-3573-4568, Lama Zubirán, Paula de la|||0000-0001-5735-9581
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/345086
Acesso em linha:https://hdl.handle.net/2117/345086
https://dx.doi.org/10.1080/10556788.2020.1841190
Access Level:acceso abierto
Palavra-chave:Interior-point methods
Stochastic optimization
Structured problems
Large-scale optimization
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
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spelling A new interior-point approach for large separable convex quadratic two-stage stochastic problemsCastro Pérez, Jordi|||0000-0003-3573-4568Lama Zubirán, Paula de la|||0000-0001-5735-9581Interior-point methodsStochastic optimizationStructured problemsLarge-scale optimizationClassificació AMS::90 Operations research, mathematical programming::90C Mathematical programmingÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativaTwo-stage stochastic models give rise to very large optimization problems. Several approaches havebeen devised for efficiently solving them, including interior-point methods (IPMs). However, usingIPMs, the linking columns associated to first-stage decisions cause excessive fill-in for the solutionof the normal equations. This downside is usually alleviated if variable splitting is applied to first-stage variables. This work presents a specialized IPM that applies variable splitting and exploits thestructure of the deterministic equivalent of the stochastic problem. The specialized IPM combinesCholesky factorizations and preconditioned conjugate gradients for solving the normal equations.This specialized IPM outperforms other approaches when the number of first-stage variables is largeenough. This paper provides computational results for two stochastic problems: (1) a supply chainsystem and (2) capacity expansion in an electric system. Both linear and convex quadratic formu-lations were used, obtaining instances of up to 38 million variables and six million constraints. Thecomputational results show that our procedure is more efficient than alternative state-of-the-art IPMimplementations (e.g., CPLEX) and other specialized solvers for stochastic optimization.This work has been supported by the grants MINECO/FEDER MTM2015-65362-R andMCIU/AEI/FEDER RTI2018-097580-B-I00. The second author was supported by theCONACyT (Consejo Nacional de Ciencia y Tecnologia, México) grant CVU-394291. Wealso thank the two anonymous reviewers, whose suggestions and comments improved thequality of the paper.Peer Reviewed20202020-11-0320212021-05-04journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/345086https://dx.doi.org/10.1080/10556788.2020.1841190reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 RTI2018-097580-B-I00 MODELIZACION Y OPTIMIZACION DE PROBLEMAS ESTRUCTURADOS DE GRAN ESCALA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3450862026-05-27T15:37:01Z
dc.title.none.fl_str_mv A new interior-point approach for large separable convex quadratic two-stage stochastic problems
title A new interior-point approach for large separable convex quadratic two-stage stochastic problems
spellingShingle A new interior-point approach for large separable convex quadratic two-stage stochastic problems
Castro Pérez, Jordi|||0000-0003-3573-4568
Interior-point methods
Stochastic optimization
Structured problems
Large-scale optimization
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
title_short A new interior-point approach for large separable convex quadratic two-stage stochastic problems
title_full A new interior-point approach for large separable convex quadratic two-stage stochastic problems
title_fullStr A new interior-point approach for large separable convex quadratic two-stage stochastic problems
title_full_unstemmed A new interior-point approach for large separable convex quadratic two-stage stochastic problems
title_sort A new interior-point approach for large separable convex quadratic two-stage stochastic problems
dc.creator.none.fl_str_mv Castro Pérez, Jordi|||0000-0003-3573-4568
Lama Zubirán, Paula de la|||0000-0001-5735-9581
author Castro Pérez, Jordi|||0000-0003-3573-4568
author_facet Castro Pérez, Jordi|||0000-0003-3573-4568
Lama Zubirán, Paula de la|||0000-0001-5735-9581
author_role author
author2 Lama Zubirán, Paula de la|||0000-0001-5735-9581
author2_role author
dc.subject.none.fl_str_mv Interior-point methods
Stochastic optimization
Structured problems
Large-scale optimization
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
topic Interior-point methods
Stochastic optimization
Structured problems
Large-scale optimization
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
description Two-stage stochastic models give rise to very large optimization problems. Several approaches havebeen devised for efficiently solving them, including interior-point methods (IPMs). However, usingIPMs, the linking columns associated to first-stage decisions cause excessive fill-in for the solutionof the normal equations. This downside is usually alleviated if variable splitting is applied to first-stage variables. This work presents a specialized IPM that applies variable splitting and exploits thestructure of the deterministic equivalent of the stochastic problem. The specialized IPM combinesCholesky factorizations and preconditioned conjugate gradients for solving the normal equations.This specialized IPM outperforms other approaches when the number of first-stage variables is largeenough. This paper provides computational results for two stochastic problems: (1) a supply chainsystem and (2) capacity expansion in an electric system. Both linear and convex quadratic formu-lations were used, obtaining instances of up to 38 million variables and six million constraints. Thecomputational results show that our procedure is more efficient than alternative state-of-the-art IPMimplementations (e.g., CPLEX) and other specialized solvers for stochastic optimization.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-11-03
2021
2021-05-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/345086
https://dx.doi.org/10.1080/10556788.2020.1841190
url https://hdl.handle.net/2117/345086
https://dx.doi.org/10.1080/10556788.2020.1841190
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 RTI2018-097580-B-I00 MODELIZACION Y OPTIMIZACION DE PROBLEMAS ESTRUCTURADOS DE GRAN ESCALA Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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