Maximal inner boxes in parametric AE-solution sets with linear shape
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Maximal inner boxes in parametric AE-solution sets with linear shape
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-10660S" target="_blank" >GA13-10660S: Interval methods for optimization problems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Computation
ISSN
0096-3003
e-ISSN
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Volume of the periodical
270
Issue of the periodical within the volume
January
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
606-619
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-84941243895