Chance constrained problems: a bilevel convex optimization perspective

TL;DR

This paper reformulates chance constrained problems as bilevel convex problems, providing a tractable penalty method and an open-source Python toolbox for efficient solutions in uncertain decision-making scenarios.

Contribution

It introduces an exact bilevel reformulation of chance constraints and develops a practical penalty approach with a bundle algorithm, along with an accessible software implementation.

Findings

Reformulation as bilevel convex problems enables efficient optimization.

Proposed penalty method effectively solves non-convex chance constrained problems.

Open-source toolbox facilitates practical application and testing.

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.