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DOI: 10.4230/DagSemProc.05031.14
URN: urn:nbn:de:0030-drops-2115
URL: https://drops.dagstuhl.de/opus/volltexte/2005/211/
Norkin, Vladimir ; Onischenko, Boris.
Minorant methods for stochastic global optimization
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Abstract
We develop numerical methods for solution of stochastic global optimization problems: min$[F(x)=Ef(x,¦Ø)| xin X]$ and $min[F(x)=P{f(x, ¦Ø) ¡Ü0} | xin X]$, where x is a finite dimensional decision vector with possible values in the set X, ¦Ø is a random variable, $f(x,¦Ø)$ is a nonlinear function of variable x, E and P denote mathematical expectation and probability signs respectively.These methods are based on the concept of stochastic tangent minorant, which is a random function $¦Õ(x,y, ¦Ø)$ of two variables x and y with expected value $¦µ(x,y)=E ¦Õ(x,y, ¦Ø)$ satisfying conditions: (i) $¦µ(x,x)=F(x)$, (ii) $¦µ(x,y) ¡ÜF(x)$ for all x,y. Tangent minorant is a source of information on a function global behavior. We develop a calculus of (stochastic) tangent minorants.
We develop a stochastic analogue of Pijavski¡¯s global optimization method and a branch and bound method with stochastic minorant bounds.
Applications to optimal facility location and network reliability optimization are discussed.
BibTeX - Entry
@InProceedings{norkin_et_al:DagSemProc.05031.14,
author = {Norkin, Vladimir and Onischenko, Boris.},
title = {{Minorant methods for stochastic global optimization}},
booktitle = {Algorithms for Optimization with Incomplete Information},
pages = {1--9},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2005},
volume = {5031},
editor = {Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2005/211},
URN = {urn:nbn:de:0030-drops-2115},
doi = {10.4230/DagSemProc.05031.14},
annote = {Keywords: Stochastic global optimization, stochastic tangent minorant, branch and bound method}
}
| Keywords: | Stochastic global optimization, stochastic tangent minorant, branch and bound method | |
| Seminar: | 05031 - Algorithms for Optimization with Incomplete Information | |
| Issue date: | 2005 | |
| Date of publication: | 14.07.2005 |
