Chance constrained problems: a bilevel convex optimization perspective

Yassine Laguel (1) , Jérôme Malick (1) , Wim Van Ackooij (2)

1 DAO - Données, Apprentissage et Optimisation
2 EDF R&D - EDF R&D

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 establish an exact reformulation of chance constrained problems as a bilevel problems with convex lower-levels. We then derive a tractable penalty approach, where 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.

Mots clés: Stochastic programming; Chance constraints; Bi-level optimization; DC programming

Domaines: Optimisation et contrôle [math.OC]

Yassine Laguel, Jérôme Malick, Wim Van Ackooij. Chance constrained problems: a bilevel convex optimization perspective. 2021. ⟨hal-03174589⟩