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

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...

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Vydáno v:Computational optimization and applications Ročník 88; číslo 3; s. 819 - 847
Hlavní autoři: Laguel, Yassine, Malick, Jérôme, van Ackooij, Wim
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2024
Springer Nature B.V
Témata:
Algorithms
Approximation
Constraints
Convex analysis
Convex and Discrete Geometry
Convexity
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Random variables
Smoothness
Statistics
DC programming
Chance constraints
Bilevel optimization
Convex optimization
Stochastic programming
ISSN:0926-6003, 1573-2894
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Shrnutí: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.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-024-00573-9