On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints
- Berthold, Holger
- Heitsch, Holger
- Henrion, René
- Schwientek, Jan
2020 Mathematics Subject Classification
- 65K05 90B05 90C15 90C17
- Probabilistic constraints, probust constraints, chance constraints, bilevel optimization, semi-infinite optimization, adaptive discretization, reservoir management
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.
- Math. Methods Oper. Res., 96 (2022), pp. 1--37 (published online on 14.12.2021), DOI 10.1007/s00186-021-00764-8 .