Algorithmic Procedures for Stochastic Optimization

  • Roger J. B. Wets
Part of the NATO ASI Series book series (volume 15)


For purposes of preliminary discussion, it is convenient to identify stochastic optimization problems with:
$$find x \varepsilon {{R}^{n}} that minimizes z = E\left\{ {f(x,{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\xi }})} \right\}$$
where ξ is a random N-vector with distribution function, P, f:Rn x RN → R U +∞ is a lower semicontinuous function, possibly convex, where dom f(.ξ) = x |f(x,ξ) is finite, corresponds to the set of acceptable choices for x when ξ is the observed value of the random vector ξ, and
$$E\left\{ {f(x,{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\xi }})} \right\} = \int {f(x,\xi ) dp(\xi )}$$


Stochastic Program Stochastic Optimization Discrete Distribution Probabilistic Constraint Lower Semicontinuous Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Roger J. B. Wets
    • 1
    • 2
  1. 1.IIASALaxenburgAustria
  2. 2.Chr. Michelsen InstituteFantoftNorway

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