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Registration Number

0222U003326, 0117U000330 , R & D reports

Title

To develop mathematical methods of modeling and making optimal robast system decisions for studying complex systems under conditions of risk and uncertainty

Head

Knopov Pavlo S.,

Registration Date

06-03-2022

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, random Markov processes and fields, mathematical methods of system risk assessment and stochastic systems modeling. Objectives: 1. To create new mathematical models and methods for estimating and forecasting crisis phenomena, monitoring and risk assessment under conditions of uncertainty. 2. Develop a new mathematical apparatus and methods for making effective robust system decisions. 3. Develop new effective methods for planning computer experiments based on modern evolutionary optimization algorithms. Research methods: methods of nonlinear non-smooth analysis, convex and non-convex stochastic programming, methods of the theory of random processes and fields, methods of large deviations for stochastic optimization problems. Results and their novelty: 1. A number of vector algorithms of branches and boundaries for discrete and continuous problems of multicriteria optimization are developed and their convergence is proved to sets of approximate solutions. 2. New mathematical methods have been developed to create systems for assessing and forecasting crisis phenomena, monitoring and choosing strategies for making robust optimal decisions in conditions of uncertainty. 3. The method of ranking threats to sustainable development in the conditions of resource deficit is constructed, the management scenarios minimizing complex risks are defined. 4. The method of empirical means is investigated, where a stationary random process with discrete or continuous time is chosen as observations, and unknown parameters satisfy a priori constraints. 5. The upper and lower limits of the probability that the Levy process, which starts from zero, remains positive are found. A variant of the saddle point method has been developed, which allows to accurately describe the asymptotic behavior of Levy distributive densities controlled by stochastic integrals.

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Ermolenko Lyubov I.
Atoev Kostyantyn L.
Bogdan Vira B.
Bila Halyna D.
Biletskyi Vasyl I.
Bogdanov Oleksandr V.
Golodnikov Oleksandr M.
Golodnikova Nina O.
Horbachuk Vasyl M.
Donets Heorgii P.
Karpets Eleonora P.
Kasytska Yevgeniia Yo.
Kyrylyuk Volodymyr S.
Knopov Oleksandr P.
Knopova Viktoriia P.
Koval V. P.
Kozlyuk Olena M.
Kolesnik Yurii S.
Koshul'ko Oleksii A.
Kuzmenko Viktor М.
Lytvynenko Fedir A.
Luk'yanov Igor O.
Norkin Volodymyr І.
Pepeliaiev Volodymyr A.
Pepeliaieva Tetiana V.
Samosonok Oleksandr S.
Chykrii Hreta T.
Oleksij Chikrii A.
Chornyi Yurii M.
Spyga Serhii P.