Maximal inner boxes in parametric AE-solution sets with linear shape

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313042" target="_blank" >RIV/00216208:11320/15:10313042 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cam.2015.07.034" target="_blank" >http://dx.doi.org/10.1016/j.cam.2015.07.034</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.amc.2015.08.003" target="_blank" >10.1016/j.amc.2015.08.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Maximal inner boxes in parametric AE-solution sets with linear shape

Popis výsledku v původním jazyce

We consider linear systems of equations A(p) x = b(p), where the parameters p are linearly dependent and come from prescribed boxes, and the sets of solutions (defined in various ways) which have linear boundary. One fundamental problem is to compute a box being inside a parametric solution set. We first consider parametric tolerable solution sets (being convex polyhedrons). For such solution sets we prove that finding a maximal inner box is an NP-hard problem. This justifies our exponential linear programming methods for computing maximal inner boxes. We also propose a polynomial heuristic that yields a large, but not necessarily the maximal, inner box. Next, we discuss how to apply the presented linear programming methods for finding large inner estimations of general parametric AE-solution sets with linear shape. Numerical examples illustrate the properties of the methods and their application.

Název v anglickém jazyce

Maximal inner boxes in parametric AE-solution sets with linear shape

Popis výsledku anglicky

We consider linear systems of equations A(p) x = b(p), where the parameters p are linearly dependent and come from prescribed boxes, and the sets of solutions (defined in various ways) which have linear boundary. One fundamental problem is to compute a box being inside a parametric solution set. We first consider parametric tolerable solution sets (being convex polyhedrons). For such solution sets we prove that finding a maximal inner box is an NP-hard problem. This justifies our exponential linear programming methods for computing maximal inner boxes. We also propose a polynomial heuristic that yields a large, but not necessarily the maximal, inner box. Next, we discuss how to apply the presented linear programming methods for finding large inner estimations of general parametric AE-solution sets with linear shape. Numerical examples illustrate the properties of the methods and their application.

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

<a href="/cs/project/GA13-10660S" target="_blank" >GA13-10660S: Intervalové metody pro optimalizační úlohy</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics and Computation

ISSN

0096-3003

e-ISSN

—

Svazek periodika

270

Číslo periodika v rámci svazku

January

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

606-619

Kód UT WoS článku

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EID výsledku v databázi Scopus

2-s2.0-84941243895