Content:
The paper examines the relationship between the solutions of a stochastic optimization problem and the solutions of large sampled versions of that problem. The question of the consistency of optimal solutions (of the sampled problems) is the main theme of this paper. A counterexample to global consistency is exhibited, but it is shown that local consistency can be guaranteed. Also, uniform consistency (robustness) of approximate solutions is examined. Even local robustness fails, unless the underlying conditions are strengthened. Sufficient conditions are displayed, and in the closing section their applicability in the context of linear recourse models is demonstrated. The paper also derives a somewhat more general strong law of large numbers for the epi-convergence of sampled problems to the original stochastic optimization problem.