English

Chance constrained problems: a bilevel convex optimization perspective

Optimization and Control 2021-03-22 v1

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 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.

Keywords

Cite

@article{arxiv.2103.10832,
  title  = {Chance constrained problems: a bilevel convex optimization perspective},
  author = {Yassine Laguel and Jérôme Malick and Wim Ackooij},
  journal= {arXiv preprint arXiv:2103.10832},
  year   = {2021}
}
R2 v1 2026-06-24T00:21:25.530Z