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Optimal scenario generation and reduction in stochastic programming

Rene Henrion(henrion***at***wias-berlin.de)
Werner Roemisch(romisch***at***math.hu-berlin.de)

Abstract: Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based on distances containing minimal information, i.e., on data appearing in the optimization model only. For linear two-stage stochastic programs we show that the optimal scenario generation problem can be reformulated as best approximation problem for the expected recourse function and as generalized semi-infinite program, respectively. The latter model turns out to be convex if either right-hand sides or costs are random. We also review the problems of optimal scenario reduction for two-stage models and of optimal scenario generation for chance constrained programs. Finally, we consider scenario generation and reduction for the classical newsvendor problem.

Keywords: stochastic programming, scenario, scenario generation, scenario reduction

Category 1: Stochastic Programming

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )

Citation: Humboldt University Berlin, Indtitute of Mathematics, February/2017

Download: [PDF]

Entry Submitted: 03/23/2017
Entry Accepted: 03/24/2017
Entry Last Modified: 03/23/2017

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