Registration Number
0212U004122,
0109U000145
, R & D reports
Title
New mathematical models of environment protection problems, the methods of its solving based on the set partitioning theory
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Head
Kiseleva Elena Mikhaylovna, Доктор фізико-математичних наук
Registration Date
30-01-2012
Organization
Dniepropetrovsk national university
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The object of the research is the theory of continuous optimal set partitioning problems (OSP) 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 an optimization theory of set functions, which part are continuous optimal set partitioning problems, and to construct new models of optimal control theory, in particular the construction of adequate mathematical models of dynamical problems of environmental protection and the corresponding theoretical apparatus for justification of these models. The paper uses concepts and methods of mathematical and functional analysis, optimization techniques, discrete mathematics, numerical methods. New mathematical models of dynamic continuous environmental protection problems are proposed. Corresponding methods and algorithms for solving dynamic continuous optimal set partitioning problems for a class of dynamical OSP problems are constructed, where the density function is unknown, however, the law of its variation with time is given: for a class of dynamical OSP problems with moving boundaries between subsets; for a class of dynamical OSP problems with moving boundaries and centers of subsets. On this basis, appropriate software, which allows us to solve certain classes of continuous dynamical environmental problems, is developed. In addition, approximation-iterative methods and algorithms for solving certain classes of optimization problems are substantiated, a theoretical basis for the construction of clustering algorithms, which take into account the entropy of the system, is developed, a method for assessing the conclusions of experts is proposed. The corresponding lemmas and theorems are given. The results can be used in solving applied ecological problems, especially problems of environmental protection: rational nature management and providing ecological safety during the design and placement of urban facilities, formation of ecological structure of the industrial region, location of the sources of pollutants and the identification of areas with sanitary and acceptable pollution standards in the construction of production facilities.
Product Description
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Балейко Наталія Вікторівна
Блюсс Олег Борисович
Бурдюк Володимир Якович
Гарт Людмила Лаврентіївна
Довгай Павло Олександрович
Дуб'яга Ольга Анатоліївна
Фірсов Олександр Дмитрович
Шевченко Тетяна Олександрівна
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2020-04-02
