@misc{PflugRuszczynskiSchultz, author = {Pflug, Georg Ch. and Ruszczynski, Andrzej and Schultz, R{\"u}diger}, title = {On the Glivenko-Cantelli Problem in Stochastic Programming: Mixed-Integer Linear Recourse}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2739}, number = {SC-97-04}, abstract = {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 expected recourse function is established.}, language = {en} } @misc{PflugRuszczynskiSchultz, author = {Pflug, Georg Ch. and Ruszczynski, Andrzej and Schultz, R{\"u}diger}, title = {On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2448}, number = {SC-96-34}, abstract = {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 hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case.}, language = {en} }