Minorant methods for stochastic global optimization

Authors Vladimir Norkin, Boris. Onischenko

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Vladimir Norkin
Boris. Onischenko

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Vladimir Norkin and Boris. Onischenko. Minorant methods for stochastic global optimization. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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.
  • Stochastic global optimization
  • stochastic tangent minorant
  • branch and bound method


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