Integrals of optimal values of random linear programming problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Uniform convergence of the approximations is proved under fairly broad conditions allowing non-convex...

Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions, it is proved that uniform convergence of empirical approximations of the right...

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original...

Models and algorithms for risk neutral and risk averse power optimization under uncertainty are presented. The approach differs from previous ones by incorporating the transmission network explicitly. Copyright Springer-Verlag 2009

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original...