Scenario tree reduction in stochastic programming with recourse for hydropower operations

Scenario reduction in stochastic programming

Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis ...

Scenario tree reduction for multistage stochastic programs

A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other. The argument is based on upper bounds of the Lr -distance and the filtration distance, and on quantitative stability results for multistage stochastic programs. The important difference from scenario r...

Scenario Reduction Algorithms in Stochastic Programming

Scenario Reduction Techniques in Stochastic Programming

Stochastic programming problems appear as mathematical models for optimization problems under stochastic uncertainty. Most computational approaches for solving such models are based on approximating the underlying probability distribution by a probability measure with finite support. Since the computational complexity for solving stochastic programs gets worse when increasing the number of atom...

Scenario reduction in stochastic programming with respect to discrepancy distances

Discrete approximations to chance constrained and mixed-integer twostage 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 red...