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. Key words: min-max stochastic programming, ambiguous chance constraints, robust optimization, uniformity principle. 1 

• Type: Journal
• Year: 2006
• Where: MP
• Authors: Alexander Shapiro
• Keywords: MP 2006, Objective Function, Stochastic Programming, Uniformity Principle