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Worst-case distribution analysis of stochastic programs

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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.

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  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332-0205, USA

    Alexander Shapiro

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  1. Alexander Shapiro
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Correspondence to Alexander Shapiro.

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Shapiro, A. Worst-case distribution analysis of stochastic programs. Math. Program. 107, 91–96 (2006). https://doi.org/10.1007/s10107-005-0680-6

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  • DOI: https://doi.org/10.1007/s10107-005-0680-6

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