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

Yassine Laguel (), Jérôme Malick () and Wim Ackooij ()
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Yassine Laguel: Université Côte d’Azur
Jérôme Malick: CNRS, LJK
Wim Ackooij: EDF R &D. OSIRIS

Computational Optimization and Applications, 2024, vol. 88, issue 3, No 4, 819-847

Abstract: 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.

Keywords: Stochastic programming; Bilevel optimization; DC programming; Chance constraints; Convex optimization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00573-9

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