Yemets Y. Research of properties of mathematical models of combinatorial optimization problems on the polyarrangements both development of a method and a algorithm of the combinatorial cutting

Object of research - combinatorial tasks of optimization and methods of their solution. A subject of research - Euclidean the combinatorial optimization tasks on the polyarrangements, methods of a solution of the Euclidean combinatorial tasks of optimization. The purpose of job - installation of new properties of the combinatorial tasks of optimization on a set of the polyarrangements, deriving of a solution of the Euclidean combinatorial tasks of optimization both in analytical, and in an algorithmic aspect. Methods of research - methods of a polyhedral theory of combinations, methods of mathematical programming. Novelty: exposition of the system of linear inequalities a convex hull of a set of the polyarrangements (polyhedron of the polyarrangements) for the first time is obtained, the structure of this set and this polyhedron is researched; the unconditional linear task of optimization on the polyarrangements is analytically solved; the estimations and sufficient conditions of minima in the unconditional tasks on the polyarrangements for the convex and strongly convex criterion functions are proved; the method of a cut for one class of the linear partially combinatorial tasks of Euclidean combinatorial optimization, as further development of a method of a combinatorial cut for the completely combinatorial tasks is offered, this method is proved. Theoretical and practical value - obtained properties of a set of the polyarrangements and polyhedron of the polyarrangements, and also the properties of the criterion functions in the tasks of optimization on the polyarrangements can be used at simulation and solution of the Euclidean combinatorial tasks of optimization, in particular, of tasks of formation of an optimal investment portofolio. From these obtained properties of the polyarrangements as the special cases turn out similar properties for permutations, polypermutations, arrangements. The results of the dissertation are used since 1996 in scientific researches of the Poltava national technical university after Ur. Kondratuk, in particular at realization of the state budget research and development project "Development of the theory, models, methods and algorithms of Euclidean combinatorial optimization", SR