On the efficient Gerschgorin inclusion usage in the global optimization alpha BB method

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313040" target="_blank" >RIV/00216208:11320/15:10313040 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10898-014-0161-7" target="_blank" >http://dx.doi.org/10.1007/s10898-014-0161-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10898-014-0161-7" target="_blank" >10.1007/s10898-014-0161-7</a>

Result language
angličtina
Original language name
On the efficient Gerschgorin inclusion usage in the global optimization alpha BB method
Original language description
In this paper, we revisit the alpha BB method for solving global optimization problems. We investigate optimality of the scaling vector used in Gerschgorin's inclusion theorem to calculate bounds on the eigenvalues of the Hessian matrix. We propose two heuristics to compute a good scaling vector , and state three necessary optimality conditions for an optimal scaling vector. Since the scaling vectors calculated by the presented methods satisfy all three optimality conditions, they serve as cheap but efficient solutions. A small numerical study shows that they are practically always optimal.
Czech name
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Czech description
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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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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

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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