Before revision:  Our primary motivation for the higher level of generality is to solve distributionally robust optimization problems with moment uncertainty. After the analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints.
After revision:  After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints.