CC BY 4.0 UnportedBerthold, HolgerHeitsch, HolgerHenrion, RenéSchwientek, Jan2022-06-202022-06-202021https://oa.tib.eu/renate/handle/123456789/9072https://doi.org/10.34657/8110We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints.enghttps://creativecommons.org/licenses/by/4.0/330510Adaptive discretizationBilevel optimizationChance constraintsProbabilistic constraintsProbust constraintsReservoir managementSemi-infinite optimizationArticle