WIAS Preprint No. 2835, (2021)

On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints


  • Berthold, Holger
  • Heitsch, Holger
    ORCID: 0000-0002-2692-4602
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Schwientek, Jan

2020 Mathematics Subject Classification

  • 65K05 90B05 90C15 90C17


  • Probabilistic constraints, probust constraints, chance constraints, bilevel optimization, semi-infinite optimization, adaptive discretization, reservoir management




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.

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