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Registration Number

0224U031519, 0121U109630 , R & D reports

Title

Develop robust methods of nonlinear and quantile regression analysis for stochastic systems in the presence of a priori constraints on unknown parameters

Head

Knopov Pavlo S., Доктор фізико-математичних наук

Registration Date

07-05-2024

Organization

V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine

Description

Object of research: Economic, ecological and technological complex systems. Problems of optimization and robust estimation, optimal control of random processes and fields, modeling of stochastic systems. Objectives: to develop fundamentally new methods of nonlinear and convex stochastic and regression analysis for problems of robust nonlinear and nonparametric estimation, modeling of equilibria, stochastic optimization and optimal decision-making under uncertainty. Research methods: methods of non-linear non-smooth analysis, convex and non-convex stochastic programming, methods of forecasting, statistical evaluation and optimal control of random processes and fields, methods of large deviations. Results and their novelty: 1. Constructions of polyhedral coherent risk measures for uncertainty conditions with ambiguity set are introduced. The obtained conditions under which their calculation, as well as distributionally-robust portfolio optimization by revenue-risk ratio, are reduced to linear programming problems. 2. Investigated problems of robust stochastic optimization with an empirical risk function by observations of a homogeneous random field. The conditions of consistency of its empirical evaluation and the convergence rate were obtained. 3. Developed methods of robust estimation of unknown distribution parameters under constraints on their moments and quantiles, applicable to applied economic and technical problems. 4. A new approach to reliability optimization using CVaR measure and bPOE probability was developed. It is used to estimate the risk of crop loss on a sown area. 5. A new approach was developed for estimating the parameters of regression models with switches, where the independent variable is time, with application to trend selection of non-stationary time series. 6. Investigated multi-nomenclature models of reservation theory with multi-component controlled stochastic processes. The structure of the optimal strategy for such systems is defined. 

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Yermolenko Liubov I.
Atoiev Kostiantyn L.
Bila Halyna D.
Bohdanov Oleksandr V.
Holodnikov Oleksandr M.
Kasytska Yevheniia Yo.
Kyryliuk Volodymyr S.
Kolesnyk Yurii S.
Norkin Volodymyr I.
Pepeliaieva Tetiana V.
Samosienok Oleksandr S.
Spyha Serhii P.