On sample average approximation for two-stage stochastic programs without relatively complete recourse

We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., problems in which there are first-stage feasible solutions that not guaranteed to have a recourse action. As feasibility measure of the SAA solution, we consider "recourse likelihood", is probability solution has For $\epsilon \in (0,1)$, demonstrate likelihood below $1-\epsilon$ converges zero exponentially fast with size. Next, analyze rate convergence optimal true problem finite region, such as bounded integer programming problems. non-finite propose modified "padded" and two cases can yield, high confidence, certain decision. Finally, conduct numerical study on resource planning illustrates results, also suggests may be room improvement some theoretical analysis.