Stability analysis for stochastic programs
Annals of Operations Research
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Rates of Convergence in Stochastic Programs with Complete Integer Recourse
SIAM Journal on Optimization
Scenario Reduction Algorithms in Stochastic Programming
Computational Optimization and Applications
Quantitative Stability in Stochastic Programming: The Method of Probability Metrics
Mathematics of Operations Research
Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints
Mathematical Programming: Series A and B
Scenario tree modeling for multistage stochastic programs
Mathematical Programming: Series A and B
A note on scenario reduction for two-stage stochastic programs
Operations Research Letters
Scenario reduction techniques in stochastic programming
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
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Discrete approximations to chance constrained and mixed-integer two-stage stochastic programs require moderately sized scenario sets. The relevant distances of (multivariate) probability distributions for deriving quantitative stability results for such stochastic programs are ℬ-discrepancies, where the class ℬ of Borel sets depends on their structural properties. Hence, the optimal scenario reduction problem for such models is stated with respect to ℬ-discrepancies. In this paper, upper and lower bounds, and some explicit solutions for optimal scenario reduction problems are derived. In addition, we develop heuristic algorithms for determining nearly optimally reduced probability measures, discuss the case of the cell discrepancy (or Kolmogorov metric) in some detail and provide some numerical experience.