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On a class of minimax stochastic Alexander Shapiro

Summary: On a class of minimax stochastic
Alexander Shapiro
and Shabbir Ahmed
School of Industrial & Systems Engineering
Georgia Institute of Technology
765 Ferst Drive, Atlanta, GA 30332.
August 29, 2003
For a particular class of minimax stochastic programming models, we
show that the problem can be equivalently reformulated into a standard
stochastic programming problem. This permits the direct use of standard
decomposition and sampling methods developed for stochastic program-
ming. We also show that this class of minimax stochastic programs is
equivalent to a large family of mean-risk stochastic programs where risk
is measured in terms of deviations from a quantile.
Key words: worst case distribution, problem of moments, Lagrangian duality,
mean risk stochastic programs, deviation from a quantile.
1 Introduction
A wide variety of decision problems under uncertainty involves optimization of


Source: Ahmed, Shabbir - School of Industrial and Systems Engineering, Georgia Institute of Technology


Collections: Engineering