On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints

Holger Berthold (), Holger Heitsch (), René Henrion () and Jan Schwientek ()
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Holger Berthold: Fraunhofer Institute for Industrial Mathematics (ITWM)
Holger Heitsch: Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
René Henrion: Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
Jan Schwientek: Fraunhofer Institute for Industrial Mathematics (ITWM)

Mathematical Methods of Operations Research, 2022, vol. 96, issue 1, No 1, 37 pages

Abstract: 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.

Keywords: Probabilistic constraints; Probust constraints; Chance constraints; Bilevel optimization; Semi-infinite optimization; Adaptive discretization; Reservoir management; 65K05; 90B05; 90C15; 90C17 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-021-00764-8

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