A robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming

dc.creatorGonzalez-Lima, MD
dc.creatorOliveira, ARL
dc.creatorOliveira, DE
dc.date2013
dc.dateDEC
dc.date2014-07-30T13:42:45Z
dc.date2015-11-26T16:31:28Z
dc.date2014-07-30T13:42:45Z
dc.date2015-11-26T16:31:28Z
dc.date.accessioned2018-03-28T23:12:32Z
dc.date.available2018-03-28T23:12:32Z
dc.identifierComputational Optimization And Applications. Springer, v. 56, n. 3, n. 573, n. 597, 2013.
dc.identifier0926-6003
dc.identifier1573-2894
dc.identifierWOS:000327240600005
dc.identifier10.1007/s10589-013-9572-5
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/53707
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/53707
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1270222
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionWe introduce an efficient and robust proposal for solving linear systems arising at each iteration of primal-dual interior-point methods for linear programming. Our proposal is based on the stable system presented by Gonzalez-Lima et al. (Comput. Opt. Appl. 44:213-247, 2009). Using similar techniques as those employed in the splitting preconditioner introduced by Oliveira and Sorensen (Linear Algebra Appl. 394:1-24, 2005) we are able to express the stable system matrix in block form such that the diagonal blocks are nonsingular diagonal matrices and the off-diagonal blocks are matrices close to zero when the iterates are close to the solution set of the linear programming problem. For degenerate problems a perturbation of the diagonal is added. We use a low-cost fixed iterative method to solve this system. Numerical experiments have shown that our approach leads to very accurate solutions for the linear programming problem.
dc.description56
dc.description3
dc.description573
dc.description597
dc.descriptionUniversidad Simon Bolivar [GID-001 DID-USB]
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionUniversidad Simon Bolivar [GID-001 DID-USB]
dc.languageen
dc.publisherSpringer
dc.publisherNew York
dc.publisherEUA
dc.relationComputational Optimization And Applications
dc.relationComput. Optim. Appl.
dc.rightsfechado
dc.rightshttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dc.sourceWeb of Science
dc.subjectLinear programming
dc.subjectPrimal-dual interior point methods
dc.subjectLinear systems
dc.subjectZero Variables
dc.subjectAlgorithm
dc.subjectEquations
dc.subjectPreconditioners
dc.subjectSolver
dc.titleA robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming
dc.typeArtículos de revistas


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