Epi-convergent scenario generation method for stochastic problems via sparse grid

Abstract

One central problem in solving stochastic programming problems is to generate moderate-sized scenario trees which represent well the risk faced by a decision maker. In this paper we propose an efficient scenario generation method based on sparse grid, and prove it is epi-convergent. Furthermore, we show numerically that the proposed method converges to the true optimal value fast in comparisonwith Monte Carlo and Quasi Monte Carlo methods.