Norkin, Vladimir ;
Onischenko, Boris.
Minorant methods for stochastic global optimization
Abstract
We develop numerical methods for solution of stochastic global optimization problems: min$[F(x)=Ef(x,Ã‚Â¦ÃƒËœ) xin X]$ and $min[F(x)=P{f(x, Ã‚Â¦ÃƒËœ) Ã‚Â¡ÃƒÅ“0}  xin X]$, where x is a finite dimensional decision vector with possible values in the set X, Ã‚Â¦ÃƒËœ is a random variable, $f(x,Ã‚Â¦ÃƒËœ)$ 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 $Ã‚Â¦Ãƒâ€¢(x,y, Ã‚Â¦ÃƒËœ)$ of two variables x and y with expected value $Ã‚Â¦Ã‚Âµ(x,y)=E Ã‚Â¦Ãƒâ€¢(x,y, Ã‚Â¦ÃƒËœ)$ satisfying conditions: (i) $Ã‚Â¦Ã‚Âµ(x,x)=F(x)$, (ii) $Ã‚Â¦Ã‚Âµ(x,y) Ã‚Â¡ÃƒÅ“F(x)$ 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 PijavskiÃ‚Â¡Ã‚Â¯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:DSP:2005:211,
author = {Vladimir Norkin and Boris. Onischenko},
title = {Minorant methods for stochastic global optimization},
booktitle = {Algorithms for Optimization with Incomplete Information},
year = {2005},
editor = {Susanne Albers and Rolf H. M{\"o}hring and Georg Ch. Pflug and R{\"u}diger Schultz},
number = {05031},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2005/211},
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 