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A new interior-point approach for large two-stage stochastic problems
dc.contributor.author | Castro Pérez, Jordi |
dc.contributor.author | Lama Zubirán, Paula de la |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa |
dc.date.accessioned | 2020-04-22T10:56:30Z |
dc.date.available | 2020-04-22T10:56:30Z |
dc.date.issued | 2020-04 |
dc.identifier.citation | Castro, J.; de la Lama, P. "A new interior-point approach for large two-stage stochastic problems". 2020. |
dc.identifier.uri | http://hdl.handle.net/2117/184307 |
dc.description.abstract | 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 |
dc.format.extent | 23 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | UPC-DEIO-JC DR 2020-01 |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització |
dc.subject.other | Interior-point methods |
dc.subject.other | Stochastic optimization |
dc.subject.other | Structured problems |
dc.subject.other | Large-scale optimization |
dc.title | A new interior-point approach for large two-stage stochastic problems |
dc.type | External research report |
dc.contributor.group | Universitat Politècnica de Catalunya. GNOM - Grup d'Optimització Numèrica i Modelització |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming |
dc.relation.publisherversion | http://www-eio.upc.edu/~jcastro/publications/reports/dr2020-01.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 27720370 |
dc.description.version | Preprint |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/RTI2018-097580-B-I00/ES/MODELIZACION Y OPTIMIZACION DE PROBLEMAS ESTRUCTURADOS DE GRAN ESCALA Y APLICACIONES/ |
local.citation.author | Castro, J.; de la Lama, P. |
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