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DOI: 10.4230/DagSemProc.05031.14
URN: urn:nbn:de:0030-drops-2115
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2005/211/
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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
Collection: 05031 - Algorithms for Optimization with Incomplete Information
Issue Date: 2005
Date of publication: 14.07.2005

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