About: Tolerance analysis in linear systems and linear programming

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.556635
Description	It is often important to know how different optimality criteria change under input data perturbations. Our aim is to compute tolerances (intervals) for the objective function and the right-hand side coefficients such that these coefficients can independently and simultaneously vary inside their tolerances while preserving the corresponding optimality criterion. We put tolerance analysis in a unified framework that is convenient for algorithmic processing and that is applicable not only in linear programming but for other linear systems as well. We propose an improvement of the known results that is optimal in some sense (the resulting tolerances are maximal and they take into account proportionality). We apply our approach to several optimality invariancies: optimal basis, support set and optimal partition invariancy. Our approach is useful not only for simplex method solvers, but for the interior points methods, too. We show that it is NP-hard to determine the maximal tolerances. It is often important to know how different optimality criteria change under input data perturbations. Our aim is to compute tolerances (intervals) for the objective function and the right-hand side coefficients such that these coefficients can independently and simultaneously vary inside their tolerances while preserving the corresponding optimality criterion. We put tolerance analysis in a unified framework that is convenient for algorithmic processing and that is applicable not only in linear programming but for other linear systems as well. We propose an improvement of the known results that is optimal in some sense (the resulting tolerances are maximal and they take into account proportionality). We apply our approach to several optimality invariancies: optimal basis, support set and optimal partition invariancy. Our approach is useful not only for simplex method solvers, but for the interior points methods, too. We show that it is NP-hard to determine the maximal tolerances. (en)
Title	Tolerance analysis in linear systems and linear programming Tolerance analysis in linear systems and linear programming (en)
skos:prefLabel	Tolerance analysis in linear systems and linear programming Tolerance analysis in linear systems and linear programming (en)
skos:notation	RIV/00216208:11320/11:10099315!RIV12-MSM-11320___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Hladík, Milan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	235482
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/11:10099315
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	sensitivity analysis; linear programming; linear systems; Tolerance analysis (en)
http://linked.open.../riv/klicoveSlovo	sensitivity analysis Tolerance analysis linear programming linear systems
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[90C126D04600]
http://linked.open...i/riv/nazevZdroje	Optimization Methods and Software
http://linked.open...in/vavai/riv/obor	BB
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	26
http://linked.open...iv/tvurceVysledku	Hladík, Milan
http://linked.open...n/vavai/riv/zamer	Moderní metody, struktury a systémy informatiky
issn	1055-6788
number of pages	16 (xsd:int)
http://bibframe.org/vocab/doi	10.1080/10556788.2011.556635
http://localhost/t...ganizacniJednotka	11320

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