Scenario Reduction with Respect to Discrepancy Distances

Zusammenfassung

As we have discussed in the previous chapters, many stochastic optimization problems do not allow for an analytic solution, and, hence, one has to resort to numerical approaches. However, numerical approaches usually require the underlying probability measures to have only a finite support. While such finite measures can be obtained, e.g., by sampling or from historical data, the number of atoms (or, scenarios) has to be in general sufficiently small to maintain the numerical tractability. Approximating a (finite) probability measure by a measure with a smaller number of atoms is denoted as scenario reduction in the literature.