Problems of choosing optimal solutions for systems with random and non-random perturbations

Abstract

The problem of choosing an optimal solution in stochastic optimization problem containing both random perturbations with given distributions and nonrandom perturbations about which only the regions of their possible values are known. As a criterion of optimality, the quantile criterion is used, i.e. The objective function value guaranteed with some given probability is optimised. This problem is closely connected with the problem of the construction confidence estimates for a statistically uncertain random vector that is a random vector with an incompletely known distribution. A concept of the generalized confidence set is used for statistically uncertain vector, and its properties are studied. The quantile stochastic optimization problem under incomplete information is solved by means of an optimal choice of the generalized confidence region. © 2017 Author(s).