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Information × Registration Number 0219U004245, 0116U002214 , R & D reports Title Theoretical foundations of mathematical models and methods for complex systems research popup.stage_title Head Kiseleva Olena Mikhaylievna, Доктор фізико-математичних наук Registration Date 18-04-2019 Organization Oles Honchar Dnipro National University popup.description2 The object of the study are the dynamical set partitioning problems with moving boundaries between subsets, the continuous problems of optimal splitting of sets with fuzzy parameters in constraints, the generalized problems of parallel ordering, the inverse problems of mechanics of a deformable solid for analysis of the prebifurcation state. The purpose of the work is the creation of mathematical models and algorithms for solving the dynamical set partitioning problems with moving boundaries between subsets and continuous problems of optimal partition of sets with fuzzy parameters in constraints, mathematical methods for generalized problems of parallel ordering, development of algorithms for solving inverse problems in mechanics thin-walled systems. Methods of research - analytical and computational methods. The main scientific results consist in the development of mathematical models and algorithms for solving continuous dynamical set partitioning problems with moving boundaries between subsets and continuous problems of optimal splitting of sets with fuzzy parameters in constraints, in the development of algorithms for solving inverse problems in the mechanics of thin-walled systems. The main scientific results are: New mathematical models were constructed and new algorithms for solving continuous dynamical set partitioning problems (FPM) with moving boundaries between subsets and continuous problems of optimal splitting of sets with fuzzy parameters in constraints were created. Various variants of the projection-iteration method, based on the conditional gradient method, are investigated to solve the conditional minimization problem of a functional in a Hilbert space. Under sufficiently general conditions of approximation of the original problem, questions of the convergence of the projection-iteration processes of approximations arising as a result of projecting into Hilbert spaces that are isomorphic to the subspaces of the original space are considered. New algorithms for solving generalized problems of parallel ordering have been developed and theoretically substantiated. For the first time algorithms have been developed to clusterize sequences of solutions corresponding to the set of postsiburcation branches of a nonlinear boundary value problem for constructing topological predictors of bifurcation. Product Description popup.authors Бойко Л. Т. Волошко В. Л. Гарт Л. Л. Говоруха В. Б. Гук Н. А. Журавель С.В. Кузенков О. О. Магас О.С. Наконечна Т. В. Притоманова О. М. Турчина В. А. Шевельова А. Є. popup.nrat_date 2020-04-02 Close