Tolerance analysis in linear systems and linear programming

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10099315" target="_blank" >RIV/00216208:11320/11:10099315 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.556635" target="_blank" >http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.556635</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/10556788.2011.556635" target="_blank" >10.1080/10556788.2011.556635</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Tolerance analysis in linear systems and linear programming

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Tolerance analysis in linear systems and linear programming

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Optimization Methods and Software

ISSN

1055-6788

e-ISSN

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Svazek periodika

26

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

16

Strana od-do

381-396

Kód UT WoS článku

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EID výsledku v databázi Scopus

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