Worst-case distribution analysis of stochastic programs
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.
uniformity principle min-max stochastic programming ambiguous chance constraints robust optimization