1. O.A. Berezovskyi, Т.O. Bardadym, E.O. Lykhovyd
ON MINIMIZATION OF QUADRATIC FUNCTION ON A POLYHEDRAL CONE
Dual bounds calculated with the use of functionally redundant constraints received by pairwise multiplication of original
linear constraints are used for finding the minimum value of quadratic function on a polyhedral cone. Necessary and
sufficient condition for finding an exact value of the global minimum is formulated.
2. G.Ts. Chikrii
ON TIME EXTENSION IN DIFFERENTIAL GAMES UNDER INTEGRAL CONSTRAINTS
The linear differential game of pursuit under integral constraints on controls is сonsidered on the basis of the time
extension principle. Sufficient conditions on the finite-time termination of the game are obtained. A model example is
given.
3. I.S. Rappoport
ONE GENERALIZATION OF THE INVERSE IMAGE THEOREM
The L  B  B -measurabiliti of the graphs of special set-valued maps, which play an important role in the construction
of control over dynamic objects on the basis of the measurable choice theorems and ensure the superimposed L measurability in gaming problems, is established.
4. V.I. Biletsky, G.A. Donets, E.I. Nenakhov
COMBINATORIAL RECOGNITION. THE PROBLEMS AND THEIR SOLVING
The bounded and unbounded combinatorial recognition problems are defined. Using a problem of switches as an example,
we show how to divide the subset of switches into groups so that by minimal number of tests the given number of faulty
switches could be found. We also consider the problem of choosing the number of same type elements of the two given
sets. For every problem we give evaluating formulas for minimal number of tests.
5. A.A. Belousov
DIFFERENTIAL GAMES UNDER GENERAL INTEGRAL CONSTRAINS ON CONTROLS
Linear systems under general convex integral constraints on controls are discussed in this paper. Analog of Pontryagin’s
Condition is formulated. On its basis sufficient conditions of the game termination in a certain guaranteed time are
obtained.
6. G.D. Bila
THE ESTIMATOR CONSISTENCY OF THE UNKNOWN PARAMETERS IN THE MODELS WITH STRONGLY
DEPENDENT NOISE
We consider the non-linear regression model with almost periodic function and random noise, assuming the noise is a
local functional of Gaussian stationary process with long-range dependence. We investigated periodogram estimations of
unknown parameters for the function in a given model and we proved their consistency.
7. G.A. Shulinok
ABOUT SHORTEST PATHS IN NUMERICAL GRAPHS
Natural Modular Graphs are considered. A problem to find paths in such graphs is investigated. Algorithms to solve this
problem are proposed.
8. V.M. Kuzmenko, V.V. Boyko
SOLVING NONCONVEX OPTIMIZATION PROBLEMS BY PNK-METHOD
An opportunity for solving nonconvex optimization problems by PNK-method is considered. This method uses variable
piecewise linear approximation for functions and finds exact penalty multiplier for constraints. Convergence conditions to
local optimum are studied. Results of computational experiments are added.
9. V.M. Mykhalevich
OPTIMALITY COMBINING THE PRINCIPLES OF GUARANTEED
AND BEST RESULTS IN THE PROBLEM OF DECISION MAKING
Proposed is a model of expexted utility on probability mass, whose formalism is based on the formally-logical principles
of optimality, unlike the SEU model by Anscombe ans Aumann defined in behaviouristic traditions.
10. A.G. Donets, I.E. Shulinok
A SOLUTION OF DUAL COLOR LINEAR MOSAIC CONSTRUCTION PROBLEM
The problem of construction of the linear mosaic for dual color templates is considered. Two templates are considered
first, then variable templates number. Appropriate linear equations are compounded and solved then.
11. V.O. Rudyk
ANT COLONY OPTIMIZATION ALGORITHMS FOR PROTEIN FOLDING PROBLEM ANALYSIS
The Hydrophobic-Hydrophilic protein folding model is examined, the algorithm based on ACO optimization method is
proposed and analyzed for protein tertiary structure prediction. The molecule model is considered to be a chain whose
monomers are placed on the vertices of 3D triangular lattice. The a priori position estimation method and pheromone trails
updating method are deviced, computational experiment confirms their appropriateness.
12. Yu.P. Laptin
SOME QUESTIONS FOR DETERMINING THE VALUES OF NONSMOOTH PENALTY FUNCTIONS
We consider an approach to construct an automatic procedure for determining the values of penalty coefficients in the
process of optimization algorithm. Connections with known results are analized.
13. O.M. Driyeva, S.P. Shpyga, O.P. Knopov
ON SOME PROPERTIES OF AN ESTIMATOR FOR THE DRIFT COEFFICIENT
OF A STOCHACTIC DIFFERENTIAL EQUATION ON THE PLANE
A stochastic differential equation with respect to fBm on the plane is considered. We study the maximum likelihood
estimator for the drift coefficient. We assume that the coefficient belongs to a given compact set of functions and prove the
strong consistency of the estimator.
14. V.B. Pavlenko
PAINTING PLANE TRIANGULATIONS
The article proposes an approach that can be useful in solving the problem of coloring planar graphs with four colors.
15. Yu.A. Pasenchenko, M.Yu. Sheverda
USING THREE-SECTORAL MODEL FOR PROGNOSTICATION OF STRUCTURAL CHANGES IN ECONOMY OF
UKRAINE
The problems of searching optimum trajectory of Ukrainian economy growing are examined, moving of investment and
labour resources between sectors with the purpose of output on such trajectory. An analysis is conducted on the basis of
three-sectoral model of economy, developed by V.A. Kolemaev.
16. L.N. Kolechkina, E.A. Dvernaya
THE MODIFY APPROACH TO THE SOLVING OF AN EXTREMAL PROBLEMS ON COMBINATORIAL CONFIGURATIONS WITH
MULTICRITERION CONDITION
Combinatorial optimization problem in combinatorial configuration permutations with additional restrictions is
considered. The method of solving such problems by using graph theory, taking into account the properties and structure
of the set of permutations is analyzed. Subprogram of the method of searching configuration’s points that uses the
coordinate method for solving the proposed modified approach is described. This subprogram searches the point of
satisfying the additional constraints of the task. Building a sequence of functions-limit’s values, decomposition points of
permutations on subgraphs polyhedra according to the coordinate method with an example of numerical experiment are
justified.
17. E.P. Karpets, G.F.Kikot, S.V. Panasenko
SHADOW ECONOMY PROCESS MODELLING ON BASIS OF INPUT-OUTPUT TABLES
The possible approaches, and evaluation of process modelingshadowing of the economy.
Proposed use kachetve research method issues a set of methods of forming and realization of the table, Input-Output.
Comparison of money on individual sectors of the economy with appropriate evidence of financial statistics reveals the
shadowy elementsof the economy.
18. N.G. Zhurbenko, B.M. Chumakov
PROGRAM CONTROL OF DILATION COEFFICIENTS OF r -ALGORITHM
The description of a family of minimization algorithms using space dilation operation along the direction of the difference
of two successive subgradients is given. In contrast to r-algorithm, in the proposed modifications the values of dilation
coefficients at each iteration are calculated in the process of algorithm. The algorithms do not require usage of the onedimensional descent procedure along direction and can be used with a constant step size.
19. V.M. Gorbachuk, G.O. Shulinok
GRANGER CAUSALITY
The methods of forecasting and Granger causality search are proposed, based upon practical examples of time series.
20. V.V. Gorin, V.M. Lyutenko
IMPLEMENTATION AND OPTIMIZATION OF REED-SOLOMON ALGORITHM FOR ERASURE CODING
PURPUSE
Various aspects for building, implementing and optimization of classic Reed-Solomon erasure coding algorithm discussed.
Detailed view into possibilities for algorithm speed improvement, question about 32 and 64-bit arithmetic usage efficiency
is given. It is shown, that for classical algorithm version the use of long words (32 and 64 bits) is not efficient despite the
fact, that size of data processed per one processor operation is proportional to the arithmetic word size.
21. D.V. Levchiy, V.A. Zaslavsky, E.I. Nenakhov
MODELING BUILDING HEATING PROCESSES FOR DETERMINATION WAYS OF ENERGY SAVING
This article provides an example of a mathematical model of process of heat loss in residential high-rise building in order
to calculate the optimal combination of power gas-fired boiler and heat pump, in order to minimize the cost of installing
the system and operating costs during life cycle.
22. T.A. Lazebna
DYNAMICS TASKS OF IMMUNE PROCESS UNDER SECONDARY ANTIGEN INTRODUCTION
The aspects of mathematical modelling of humoral immune reaction under secondary antigen introduction have been
investigated in consideration of affinity of cells receptors involved in immune process. The numerical investigation results
of dynamics tasks are presented.
23. P.I. Stetsyuk
ACCELERATION OF POLYAK’S SUBGRADIENT METHOD
The properties of Polyak’s subgradient method for finding the minimum point of a convex function is investigated. It is
shown that for ravine functions the convergence of the method can be accelerated by a linear transformation of the space
of variables. Polyak’s subgradient method with the transformation of the space in the case of the obtuse angle between two
successive subgradients is considered. It significantly reduces the number of iterations for smooth and nonsmooth ravine
functions.