Optimal and suboptimal solutions to stochastically uncertain problems of quintile optimization

In this paper, problems of stochastic optimization under incomplete information on distribution of random perturbations with the quintile and probability criteria are considered. The minimax approach is used when optimal solutions are chosen. Conditions for equivalency of direct and inverse problems of stochastic optimization under incomplete statistical information are studied. The solution method for statistically uncertain problems of optimization with the quintile criterion basing on the use of generalized confidence sets for statistically uncertain random quantities is proposed. The use of confidence sets for finding suboptimal solutions to the problem of stochastic optimization under incomplete information is considered. Examples of the application of obtained relations are represented.