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Chance-constrained programs with convex underlying functions: a bilevel convex optimization perspective

Author

Listed:
  • Yassine Laguel

    (Université Côte d’Azur)

  • Jérôme Malick

    (CNRS, LJK)

  • Wim Ackooij

    (EDF R &D. OSIRIS)

Abstract

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness, optimizing over a chance constrained set is challenging. In this paper, we consider chance constrained programs where the objective function and the constraints are convex with respect to the decision parameter. We establish an exact reformulation of such a problem as a bilevel problem with a convex lower-level. Then we leverage this bilevel formulation to propose a tractable penalty approach, in the setting of finitely supported random variables. The penalized objective is a difference-of-convex function that we minimize with a suitable bundle algorithm. We release an easy-to-use open-source python toolbox implementing the approach, with a special emphasis on fast computational subroutines.

Suggested Citation

  • Yassine Laguel & Jérôme Malick & Wim Ackooij, 2024. "Chance-constrained programs with convex underlying functions: a bilevel convex optimization perspective," Computational Optimization and Applications, Springer, vol. 88(3), pages 819-847, July.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:3:d:10.1007_s10589-024-00573-9
    DOI: 10.1007/s10589-024-00573-9
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    References listed on IDEAS

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