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Minorant methods for stochastic global optimization Norkin, Vladimir Onischenko, Boris. Stochastic global optimization stochastic tangent minorant branch and bound method 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Vladimir Norkin and Boris. Onischenko 2005 Is Part Of Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.05031.14 urn:nbn:de:0030-drops-2115 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.14 eng https://creativecommons.org/licenses/by/4.0/legalcode