Comparing structured ambiguity sets for stochastic optimization: Application to uncertainty quantification
L. Chaouach (TU Delft - Team Dimitris Boskos)
T.A.E. Oomen (TU Delft - Team Jan-Willem van Wingerden)
D. Boskos (TU Delft - Team Dimitris Boskos)
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Abstract
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 Wasserstein 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.