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.