Comparing structured ambiguity sets for stochastic optimization: Application to uncertainty quantification

The aim of this paper is to compare two classes of structured ambiguity sets, which are data-driven and can reduce the conservativeness of their associated optimization problems. These two classes of structured sets, coined Wasser-stein hyperrectangles and multi-transport hyperrectangles, are explored in their trade-offs in terms of reducing conservativeness and providing tractable reformulations. It follows that multi-transport hyperrectangles lead to tractable optimization problems for a significantly broader range of objective functions under a decent compromise in terms of conservativeness reduction. The results are illustrated in an uncertainty quantification case study.