Minimax analysis of stochastic problems

Minimax analysis of stochastic problems

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Article ID: iaor20031198
Country: United Kingdom
Volume: 17
Issue: 3
Start Page Number: 523
End Page Number: 542
Publication Date: May 2002
Journal: Optimization Methods & Software
Authors: ,
Abstract:

In practical applications of stochastic programming the involved probability distributions are never known exactly. One can try to hedge against the worst expected value resulting from a considered set of permissible distributions. This leads to a min–max formulation of the corresponding stochastic programming problem. We show that, under mild regularity conditions, such a min–max problem generates a probability distribution on the set of permissible distributions with the min–max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution. We consider examples of the news vendor problem, the problem of moments and problems involving unimodal distributions. Finally, we discuss the Monte Carlo sample average approach to solving such min–max problems.

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