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Т еор ія о птим а ль н их р іш е нь Збірник наукових праць Заснований в 1967 р. Виходить 1 раз на рік 2016 Abstracts of articles in English O.S. Samosonok, G.D. Bila, A.P. Knopov USAGE OF MARKOV RANDOM FIELDS FOR ROOT COUSE DETERMINATION OF NETWORK FAULT The model of the communication network based on Markov fields is considered along with the problem of identification of hidden network’s fault based on Bayesian principle of recognition. A recursive algorithm for identifying the root causes of communication system faults is suggested based on analysis of the fault messages registered in the neighboring nodes of the network topological graph. G.A. Donets, A.N. Naghirna OPTIMIZATION OF QUADRATIC FUNCTION ON A SET OF PERMUTATIONS Approach to the solution of optimization problems with quadratic function of the purpose is considered on the combinatorial set of permutations, represented as a graph. The numerical example is given. L.F. Hulianytskyi, I.I. Riasna ON FORMALIZATION OF COMBINATORIAL OPTIMIZATION PROBLEMS ON FUZZY SETS The article considers an approach to formalizing the concept "fuzzy combinatorial object" that allows to formalize both known, and new classes of problems of combinatorial optimization on fuzzy sets. We classify fuzzy combinatorial objects. Examples of such fuzzy combinatorial objects as fuzzy arrangements, fuzzy combinations, fuzzy permutations, and fuzzy graphs are given. M.F. Semeniuta ON DISTANCE ANTIMAGIC LABELING OF GRAPHS We studied the antimagic type of a vertex labeling of the graph. We have found necessary condition for existence of (a, d)-distance antimagic labelling for circulation graphs, as well as necessary and sufficient conditions for existence of (a, d)-distance antimagic labelling for a Dutch windmill graph. V.K. Chikriy ONE GAME MODEL OF THE SPORT SINGLE COMBAT A game problem on the sport single combat is explored on the basis of the method of resolving functions. Sufficient conditions for winning of each of the players are established, expressed in the terms of parameters of the conflict-controlled process under study. I.E. Shulinok, G.A. Shulinok ABOUT NUMERIC GRAPHS NODES MATCHING Natural arithmetic and natural modular graphs are considered. The graphs qualities for cover problem are solved. The algorithms to allow compute coverability of NA- and NM-graphs were developed. Also algorithms to compute minimal cover for any NA- and NM-graph were made and appropriate statements were proved. I.S. Rappoport ON THE REGULARIZATION OF INTEGRANTS Minimum conditions of reguiar integrants for the existence of integral functionals and the possibility of regularization of integrants while maintaining extreme value of integral functionals is established. M.M. Kopets, S. F. Sabol OPTIMAL CONTROL BY PROCESS OF VIBRATION OF THE PRISMATIC BEAM In the present paper the linear-quadratic optimal control problem for vibration process of the prismatic is considered. The necessary optimality conditions are obtained by using the Lagrange multiplier method. The system of integro-differential Riccati equations is derived from this conditions. The solution of obtained system permits to write the closed formula for optimal control. S.I. Dotsenko ON EXPENSES DISTRIBUTION IN CONVEYING PROBLEM The expenses distributions in conveying problem is considered at the conditions, that the total customers demand doesn't exceed vehicle bearing capacity. The acceptable decision is found with the help of cooperative game theory technique. V.I. Biletsky, E.I. Nenakhov ALGORITHMS OF SEARCHING FOR TWO ACTIVE BALLS ON GIVEN SETS The problems of searching for two active balls on given sets for n=63, 89. We some give theorems that allow calculating the minimal number of trials needed to find two active balls among the elements of the given set. For every case, the specific step-by-step algorithms are provided. A.N. Khimich, A.V. Popov, А.Y. Baranov, A.V. Chystyakov HYBRID ALGORITHM FOR SOLVING EIGENVALUES PROBLEM FOR BAND MATRICES This paper proposes an algorithm for solving partial generalized algebraic eigenvalue problem with band symmetric matrices on hybrid computers. The results of testing of the algorithm on a personal hybrid supercomputer Inparkom_pg are shown. P.І. Stetsyuk, E.S. Dolynskyi, I.I. Parasiuk ON THE SHORTEST K-NODE PATH IN A DIRECTED GRAPH We present the formulation of the mixed Boolean linear programming problem for the shortest path, which passes through the given number of nodes of the digraph. The results of numerical experiments of solution of discrete programming problems using NEOS-solver are given. We discuss the formulation of the problem for finding the shortest Hamiltonian path in a directed graph. Yu.N. Bazilevich ON THE REDUCING OF SEMIDEFINITE PROGRAMMING PROBLEM The method, which allows to reducing some symmetric matrices to the same block-diagonal form, either to establishing that such a reduction is impossible for these matrices, is considered. This can be useful in solving semidefinite programming problems. We taken into account the demand — the transformation matrix must be orthogonal. O.P. Lykhovyd, O.V. Fesyuk MPI-REALIZATION OF AN ALGORITHM FOR SOLVING THE PROBLEM OF FINDING LOAD OF POWER SYSTEM The problem of finding optimal load of power units with a non-smooth nonlinear fuel cost function, which takes into account the valve point loading effect, is considered. Parallel MPI-realization of an algorithm for solving the problem and the results of computational experiments are presented. V.I. Norkin, I.G. Magdenko, B.V. Norkin NUMERICAL SIMULATION OF THE INSURANCE BUSINESS BY MEANS OF MARKOV CHAINS A model of evolution of an insurance company's capital in the form of a Markov chain with a large number (thousands) of states is developed. To construct the transition probability matrix quarterly or annual statistics of the company’s premiums and claims is used. This statistic accounts for correlation of premiums and claims. Markov chains method allows effectively compute not only the probability of ruin of the company as a function of time, but also visually track the evolution of the distribution of company’s capital over time. A.G. Donets, S.P. Zagordniuk CONSTRUCTING A TWO-DIMENSIONAL MOSAIC BY MEANS OF ONE PATTERN We consider the problem of constructing discrete images on a rectangular field by means of patterns. A notion of pattern self-sufficiency is introduced, which means that one can construct there identity image by means of the pattern. We prove several statements about necessary and sufficient conditions for patterns possessing this property. V.M. Kuzmenko, E.I. Nenakhov A REDUCTION OF SUPERQUANTILE ERROR TO ROCKAFELLAR ERROR IN REGRESSION ANALISYS An opportunity of reduction of superquantile error to Rockafellar error for uniform discrete distribution is considered. Two variants of reduction are shown and a question of equivalence of using superquantile error and reductions is analyzed. N.G. Zhurbenko THE CONSTRUCTION OF LINEAR CLASSIFIERS ON THE BASIS OF SUPPORT FUNCTIONS An algorithm for construction of linear binary classifiers is proposed. The objects of recognition are presented by convex compacts of Euclidean space. The algorithm is based on the use of support functions of convex compacts and nonsmooth optimization methods. G.A. Donets, L.N. Kolechkina AN APPROACH SOLUTION EXTREME PROBLEMS ON COMBINATORIAL CONFIGURATIONS IN GRAPHS We consider the optimization problem of combinatorial optimization configurations permutations, describes the approach to the solution of these problems on the basis of graph theory to the properties and structure of the set of permutations. An algorithm for solving such problems. O.E. Skukis INFORMATION TECHNOLOGIES AND SYSTEMS OF VEHICLE LOGISTICS Analysis of information systems (IS) of vehicle logistics. The structure and composition of IS designed for automation of manufacturing processes of enterprises operating in the segment of logistics and transportation management. V.M. Gorbachuk, G.O. Shulinok, O.O. Morozov NETWORK EFFICIENCY ESTIMATION It is shown the efficiency of networks is estimated on the basis of their organization as decentralized systems.