An extension of the αBB-type underestimation to linear parametric Hessian matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10329229" target="_blank" >RIV/00216208:11320/16:10329229 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10898-015-0304-5" target="_blank" >http://dx.doi.org/10.1007/s10898-015-0304-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10898-015-0304-5" target="_blank" >10.1007/s10898-015-0304-5</a>
Alternative languages
Result language
angličtina
Original language name
An extension of the αBB-type underestimation to linear parametric Hessian matrices
Original language description
The classical method is a global optimization method the important step of which is to determine a convex underestimator of an objective function on an interval domain. Its particular point is to enclose the range of a Hessian matrix in an interval matrix. To have a tighter estimation of the Hessian matrices, we investigate a linear parametric form enclosure in this paper. One way to obtain this form is by using a slope extension of the Hessian entries. Numerical examples indicate that our approach can sometimes significantly reduce overestimation on the objective function. However, the slope extensions highly depend on a choice of the center of linearization. We compare some naive choices and also propose a heuristic one, which performs well in executed examples, but it seems there is no one global winner.
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Global Optimization
ISSN
0925-5001
e-ISSN
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Volume of the periodical
64
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
217-231
UT code for WoS article
000369249300003
EID of the result in the Scopus database
2-s2.0-84957430321