USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD

Detalhes bibliográficos
Autor(a) principal: Berti,Lilian F.
Data de Publicação: 2016
Outros Autores: Oliveira,Aurelio R.L., Ghidini,Carla T.L.S.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382016000300487
Resumo: ABSTRACT Interior point methods have been widely used to determine the solution of large-scale linear programming problems. The predictor-corrector method stands out among all variations of interior point methods due to its efficiency and fast convergence. In each iteration it is necessary to solve two linear systems to determine the predictor-corrector direction. Solving such systems corresponds to the step which requires more processing time, and therefore, it should be done efficiently. The most common approach to solve them is the Cholesky factorization. However, Cholesky factorization demands a high computational effort in each iteration. Thus, searching for effort reduction, the continued iteration is proposed. This technique consists in determining a new direction through projection of the search direction and it was inserted into PCx code. The computational results regarding medium and large-scale problems, have indicated a good performance of the proposed approach in comparison with the predictor-corrector method.
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spelling USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHODinterior point methodslinear programmingcontinued iterationABSTRACT Interior point methods have been widely used to determine the solution of large-scale linear programming problems. The predictor-corrector method stands out among all variations of interior point methods due to its efficiency and fast convergence. In each iteration it is necessary to solve two linear systems to determine the predictor-corrector direction. Solving such systems corresponds to the step which requires more processing time, and therefore, it should be done efficiently. The most common approach to solve them is the Cholesky factorization. However, Cholesky factorization demands a high computational effort in each iteration. Thus, searching for effort reduction, the continued iteration is proposed. This technique consists in determining a new direction through projection of the search direction and it was inserted into PCx code. The computational results regarding medium and large-scale problems, have indicated a good performance of the proposed approach in comparison with the predictor-corrector method.Sociedade Brasileira de Pesquisa Operacional2016-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382016000300487Pesquisa Operacional v.36 n.3 2016reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/0101-7438.2016.036.03.0487info:eu-repo/semantics/openAccessBerti,Lilian F.Oliveira,Aurelio R.L.Ghidini,Carla T.L.S.eng2017-02-14T00:00:00Zoai:scielo:S0101-74382016000300487Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2017-02-14T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
title USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
spellingShingle USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
Berti,Lilian F.
interior point methods
linear programming
continued iteration
title_short USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
title_full USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
title_fullStr USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
title_full_unstemmed USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
title_sort USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD
author Berti,Lilian F.
author_facet Berti,Lilian F.
Oliveira,Aurelio R.L.
Ghidini,Carla T.L.S.
author_role author
author2 Oliveira,Aurelio R.L.
Ghidini,Carla T.L.S.
author2_role author
author
dc.contributor.author.fl_str_mv Berti,Lilian F.
Oliveira,Aurelio R.L.
Ghidini,Carla T.L.S.
dc.subject.por.fl_str_mv interior point methods
linear programming
continued iteration
topic interior point methods
linear programming
continued iteration
description ABSTRACT Interior point methods have been widely used to determine the solution of large-scale linear programming problems. The predictor-corrector method stands out among all variations of interior point methods due to its efficiency and fast convergence. In each iteration it is necessary to solve two linear systems to determine the predictor-corrector direction. Solving such systems corresponds to the step which requires more processing time, and therefore, it should be done efficiently. The most common approach to solve them is the Cholesky factorization. However, Cholesky factorization demands a high computational effort in each iteration. Thus, searching for effort reduction, the continued iteration is proposed. This technique consists in determining a new direction through projection of the search direction and it was inserted into PCx code. The computational results regarding medium and large-scale problems, have indicated a good performance of the proposed approach in comparison with the predictor-corrector method.
publishDate 2016
dc.date.none.fl_str_mv 2016-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382016000300487
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382016000300487
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0101-7438.2016.036.03.0487
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.36 n.3 2016
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
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