On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints - Berthold, Holger; Heitsch, Holger; Henrion, René; Schwientek, Jan (Mathematical methods of operations research (Heidelberg, Germany), 2022)
We 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.