A New Approach For Finding A Basis For The Splitting Preconditioner For Linear Systems From Interior Point Methods

dc.creatorSunagua
dc.creatorPorfirio; Oliveira
dc.creatorAurelio R. L.
dc.date2017
dc.datemaio
dc.date2017-11-13T13:13:06Z
dc.date2017-11-13T13:13:06Z
dc.date.accessioned2018-03-29T05:51:11Z
dc.date.available2018-03-29T05:51:11Z
dc.identifierComputationall Optimization And Applications. Springer, v. 67, p. 111 - 127, 2017.
dc.identifier0926-6003
dc.identifier1573-2894
dc.identifierWOS:000398939500004
dc.identifier10.1007/s10589-016-9887-0
dc.identifierhttps://link-springer-com.ez88.periodicos.capes.gov.br/article/10.1007%2Fs10589-016-9887-0
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/327001
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1364026
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionThe class of splitting preconditioners for the iterative solution of linear systems arising from Mehrotra's predictor-corrector method for large scale linear programming problems needs to find a basis through a sophisticated process based on the application of a rectangular LU factorization. This class of splitting preconditioners works better near a solution of the linear programming problem when the matrices are highly ill-conditioned. In this study, we develop and implement a new approach to find a basis for the splitting preconditioner, based on standard rectangular LU factorization with partial permutation of the scaled transpose linear programming constraint matrix. In most cases, this basis is better conditioned than the existing one. In addition, we include a penalty parameter in Mehrotra's predictor-corrector method in order to reduce ill-conditioning of the normal equations matrix. Computational experiments show a reduction in the average number of iterations of the preconditioned conjugate gradient method. Also, the increased efficiency and robustness of the new approach become evident by the performance profile.
dc.description67
dc.description1
dc.description111
dc.description127
dc.descriptionCNPq
dc.descriptionFAPESP
dc.descriptionUMSA
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.languageEnglish
dc.publisherSpringer
dc.publisherNew York
dc.relationComputationalL Optimization and Applications
dc.rightsfechado
dc.sourceWOS
dc.subjectLinear Programming
dc.subjectSplitting Preconditioner
dc.subjectRectangular Lu Factorization
dc.subjectTranspose Basis
dc.titleA New Approach For Finding A Basis For The Splitting Preconditioner For Linear Systems From Interior Point Methods
dc.typeArtículos de revistas


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