Registration Number
0222U003166,
0119U100337
, R & D reports
Title
Mathematical modeling and optimization of dynamic systems for defense, ecology and medicine.
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Head
Lyashko Sergei I., Доктор фізико-математичних наук
Registration Date
19-02-2022
Organization
Taras Shevchenko National University of Kyiv
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Object of research: Computer programs for algorithms for solving variational inequalities, multilevel variational problems and fast learning of neural networks. Computer programs for modeling averaged models of multiphase diffusion in porous media. Algorithms for solving the problem of optimal control to clarify the external ballistic parameters.
Objective: The aim of the project is to develop computer programs for algorithms for solving variational inequalities, multilevel variational problems and rapid learning of neural networks, modeling averaged models of multiphase diffusion in porous media and solving optimal control problems to refine external ballistic parameters.
Research method: finite-difference method, schemes of fast Nesterov gradient method, methods of a priori estimates in negative spaces, methods of averaging differential equations in partial derivatives.
An algorithm for modeling and optimizing the Richards-Klut equation is constructed. Popov's two-stage Bregman method with a new adaptive rule for choosing the step value, which does not require knowledge of Lipschitz constants and calculation of operator values at additional points, has been studied. Two new approximate algorithms with Bregmann projection have been developed to solve variational inequalities in Hilbert space. A new direct-dual algorithm for two-level convex programming problems with quadratic functions in internal problems has been developed. The averaged initial-boundary value problems are constructed and substantiated, the solutions of which approach the solutions of this initial-boundary value problem, which simulates the processes of multiphase diffusion and filtration in porous media.
Product Description
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Byelousova Olena А.
Veklych Olena A.
Gulianytskyi Leonid F
Kivva Tetyana S.
Klyushyn Dmitro A.
Potapenko Leonid I.
Sirenko Ihor Р.
Sandrakov Gennadij V.
Semenov Volodymyr V.
Stelya Оleg B.
Tereschenko Yaroslav V.
Tymoshenko Andriy А.
Cherniy Dmytro I.
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2022-03-09
