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0215U003364,
0112U000193
,
Mathematical models and methods of complex systems' optimization on the base of nonlinear set partitioning theory
Kiseleva Elena Mikhaylovna, Доктор фізико-математичних наук
28-01-2015
Dniepropetrovsk national university
The object of the research is the theory of continuous optimal set partitioning problems (SPP) as an infinite-dimensional nonclassical problems of mathematical programming with boolean variables. The aim of the research is to solve the fundamental scientific problem, which is associated with the development of new sections of the infinite mathematical programming, namely the development of mathematical models, creation and theoretical substantiation of methods solving continuous nonlinear SPPs on n-dimensional Euclidean space; development and software implementation of algorithms based on the proposed methods; application of the developed theoretical apparatus and programs' complex to solve some practical nonlinear optimization problems. The work uses concepts and methods of mathematical and functional analysis, optimization techniques, discrete mathematics, numerical methods, differential and integral equations. New classes of nonlinear continuous SPPs, which are infinite-dimensional problems of mathematical programming with boolean variables, are proposed. The new models of such problems are constructed and analyze for fixed and unfixed centers. Transition to the dual finite-dimensional nonsmooth problems was grounded. The discovered properties of the models and problems' solutions presented as relevant theorems and lemmas. We constructed methods and algorithms for solving all kinds of proposed problems. In addition, projection-iterative methods and algorithms for solving certain classes of nonlinear optimization problems are substantiated. Applications of the results to nonlinear mathematical models of ecology are cited. All of the proposed algorithms were implemented in software languages C, C ++, C
Адлуцький Віктор Якович
Балейко Наталія Вікторівна
Бурдюк Володимир Якович
Гарт Людмила Лаврентіївна
Довгай Павло Олександрович
Дуб'яга Ольга Анатоліївна
Кузенков Олександр Олександрович
Шаповал Ірина Павлівна
Шевченко Тетяна Олександрівна
2020-04-02
Updated: 2025-12-21
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