Worst-case distribution analysis of stochastic programs

Authors:
Alexander Shapiro
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205, Atlanta, Georgia, USA
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called ``Uniformity Principle'' of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.