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

Author

Listed:
  • Holger Berthold

    (Fraunhofer Institute for Industrial Mathematics (ITWM))

  • Holger Heitsch

    (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))

  • René Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))

  • Jan Schwientek

    (Fraunhofer Institute for Industrial Mathematics (ITWM))

Abstract

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.

Suggested Citation

  • Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:1:d:10.1007_s00186-021-00764-8
    DOI: 10.1007/s00186-021-00764-8
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    References listed on IDEAS

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    5. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
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    Cited by:

    1. Xun Shen & Satoshi Ito, 2024. "Approximate Methods for Solving Chance-Constrained Linear Programs in Probability Measure Space," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 150-177, January.

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