Stopping Rules for Stochastic Decomposition

In our development thus far, we have concentrated on objective function approximations within a Stochastic Decomposition algorithm and on establishing asymptotic optimality of the solutions provided by SD. While such asymptotic properties provide the necessary analytic foundation for the algorithm, any practical computer implementation requires effective stopping criteria. It is important to recognize that when using sampled data to solve a problem, standard deterministic stopping rules are inadequate. We will develop specialized optimality tests that take advantage of the information generated during the course of the SD algorithm.