About optimization problems with probabilistic uncertainty

Abstract

Two approaches to the ordering of discrete random variables for the use in optimization problem statements are proposed. Within the first approach, the relation of a linear order on a set of discrete random variables is introduced. The second approach assumes the partition of a set of discrete random variables into equivalence classes on the basis of the comparison of their moments and the introduction of a linear order on the obtained quotient set. Some properties of the offered orders are considered. Using the introduced orders, some optimization problems, which consider the probabilistic uncertainty of data, are posed.