Artikel
On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints
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.
- Language
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Englisch
- Bibliographic citation
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Journal: Mathematical Methods of Operations Research ; ISSN: 1432-5217 ; Volume: 96 ; Year: 2021 ; Issue: 1 ; Pages: 1-37 ; Berlin, Heidelberg: Springer
- Classification
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Wirtschaft
Statistical Simulation Methods: General
- Subject
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Probabilistic constraints
Probust constraints
Chance constraints
Bilevel optimization
Semi-infinite optimization
Adaptive discretization
Reservoir management
- Event
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Geistige Schöpfung
- (who)
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Berthold, Holger
Heitsch, Holger
Henrion, René
Schwientek, Jan
- Event
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Veröffentlichung
- (who)
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Springer
- (where)
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Berlin, Heidelberg
- (when)
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2021
- DOI
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doi:10.1007/s00186-021-00764-8
- Last update
-
15.04.0003, 1:40 AM CET
Data provider
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Object type
- Artikel
Associated
- Berthold, Holger
- Heitsch, Holger
- Henrion, René
- Schwientek, Jan
- Springer
Time of origin
- 2021
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