Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/286763 
Year of Publication: 
2021
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 96 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2021 [Pages:] 1-37
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints.
Subjects: 
Probabilistic constraints
Probust constraints
Chance constraints
Bilevel optimization
Semi-infinite optimization
Adaptive discretization
Reservoir management
JEL: 
K05
B05
C15
C17
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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