Computational Complexity of Stochastic Programming: Monte Carlo Sampling Approach

For a long time modeling approaches to stochastic programming were dominated by scenario generation methods. Consequently the main computational effort went into development of decomposition type algorithms for solving constructed large scale (linear) optimization problems. A different point of view emerged recently where computational complexity of stochastic programming problems was investigated from the point of view of randomization methods based on Monte Carlo sampling techniques. In that approach the number of scenarios is irrelevant and can be infinite. On the other hand, from that point of view there is a principle difference between computational complexity of two and multistage stochastic programming problems – certain classes of two stage stochastic programming problems can be solved with a reasonable accuracy and reasonable computational effort, while (even linear) multistage stochastic programming problems seem to be computationally intractable in general. Mathematics Subject Classification (2010). Primary 90C15; Secondary 90C60.