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Algorithmic Procedures for Stochastic Optimization

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

Abstract

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
$$E\left\{ {f(x,{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\xi }})} \right\} = \int {f(x,\xi ) dp(\xi )}$$
.

Keywords

Stochastic Program Stochastic Optimization Discrete Distribution Probabilistic Constraint Lower Semicontinuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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