Improving aggregation bounds for two-stage stochastic programs

Abstract

Stochastic multi-stage linear programs are rarely used in practical applications due to their size and complexity. Using a general matrix to aggregate the constraints of the deterministic equivalent yields a lower bound. A similar aggregation in the dual space provides an upper bound on the optimal value of the given stochastic program. Jensen's inequality and other approximations based on aggregation are a special case of the suggested approach. The lower and upper bounds are tightened by updating the aggregating weights.