Duality and statistical tests of optimality for two stage stochastic programs

We present alternative methods for verifying the quality of a proposed solution to a two stage stochastic program with recourse. Our methods revolve around implications of a dual problem in which dual multipliers on the nonanticipativity constraints play a critical role. Using randomly sampled observations of the stochastic elements, we introduce notions of statistical dual feasibility and sampled error bounds. Additionally, we use the nonanticipativity multipliers to develop connections to reduced gradient methods. Finally, we propose a statistical test based on directional derivatives. We illustrate the applicability of these tests via some examples.