Sofronova M. Mathematical modeling of the placement of convex n-dimensional polytopes in an n-dimensional parallelepiped

Object of the study is the process of modeling of arranging on n-parallelepipeds and n-polytopes in the field of n-dimensional space having the form n-parallelepiped. The objective of the study is the development of constructive means of mathematical modeling, construction of mathematical models and developing approached methods for the solving optimization problems of arranging n-parallelepipeds and n-polytopes in the field of n-dimensional space having the form n-parallelepiped. The methods of geometrical designing, the Ф-functions method, modified method of optimization on groups variable, modified simplex-method and modified method of converging neighbourhoods are used. The program realization with the help of computer is carried out. Ф-functions of n-parallelepipeds and n-polytope for the first time are constructed. Is offered modified method of construction of a convex hull of the given set of points in. The decision optimization of problem of arranging on n-parallelepipeds and n-polytopes forthe first time is carried out on the basis of the developed combined methods. The of dissertation studies are used in the instruction process at the Kharkiv National University of radioelectronics, and also can be used for the solving of various problems of optimization of arranging multidimensional of objects arising in various industries at the solving of a problem of resource economy, problems of planning of experiments, and also for the solving others optimization problems, which are reduced to problems of arranging on n-parallelepipeds and n-polytopes.