On the Glivenko-Cantelli problem in stochastic programming: Linear recourse and extensions. (English) Zbl 0977.90031

Pflug, Georg Ch.; Ruszczyński, Andrzej; Schultz, Rüdiger

Math. Oper. Res. 23, No. 1, 204-220 (1998).

Summary: 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.

MSC:

90C15	Stochastic programming
60F99	Limit theorems in probability theory

Keywords:

stochastic programming; empirical measures; uniform convergence