  When there are infinitely many scenarios, the current studies of two-stage
stochastic programming problems rely on the relatively complete recourse
assumption. However, such assumption can be unrealistic for many real-world
problems. This motivates us to study general stochastic programming problems
where the sample average approximation (SAA) solutions are not necessarily
feasible. When the problems are convex and the true solutions lie in the
interior of feasible solutions, we show the portion of infeasible SAA solutions
decays exponentially as the sample size increases. We also study functions with
chain-constrained domain, and show the portion of SAA solutions having a low
degree of feasibility decays exponentially as the sample size increases. This
result is then extended to multistage stochastic programming.
