G.Ts. Chikrii
ON ONE GENERALIZATION OF PONTRYAGIN’S MODEL EXAMPLE
The game problem of meeting of two higher-order controlled objects, beeng a generalization of Pontryagin’s model
example, is solved on the basis of time-dilatation approach. Conditions on the systems parameters, sufficient for the game
termination under all initial states, are derived.
D.A. Omelianchyk
AGENT-BASED ECONOMIC MODELLING: FEATURES, TYPES, PROBLEMS
The main approaches to agent-based models design are discussed. The characteristic features and basic component of
agent-based models are defined. The notion of an «agent» is considered. The main purposes of agent-based models
construction are given. Some possible classifications are explained. The brief review of MOSES and EURACE is
presented.
I.Yu. Krivonos
ON A PURSUIT GAME WITH FRACTIONAL DYNAMIC
An example of dynamic pursuit game is studies, in which the pursuer moves according to a differetial equation of
fractional order , while evader’s equation of motion is of order e .
A.G. Donets
WHETHER ARITHMETICAL GRAPHS ARE HAMILTONIAN
This paper presents some investigations on existence Hamiltonian circle in arithmetical graphs. It was shown that only
various relations between two largest generatricsas can be used for the addressing questions. We proved some new theorems
about existence Hamiltonian circles with relations 1, 2, 3, 4.
G.A. Shulinok, I.E. Shulinok
PATH SEARCHING IN NUMERICAL GRAPHS
Natural Modular Graphs are considered. A problem to find paths in such graphs is investigated. Interaction between
natural modular graphs and linear Diophantine equations is shown. An approach to solve such equation or insolubility
justification is proposed.
B.V. Norkin
OPTIMIZATION OF AN INSURANCE BUSINESS USING PARALLEL GPU ACCELERATED SIMULATIONS
The paper considers the simulation model of an insurance company, based on the real-world financial statistics. The
model is included in an risk modeling system RMS, that utilizes NVIDIA CUDA technology for GPU acceleration.
The system is based on dynamic financial analysis principals. It allows to predict the future performance of the
company, depending on the control parameters.
L.A. Sobolenko, S.G. Nenakhova, I.A. Shubenkova
COMBINED PENALTY FUNCTION FOR CONSTRUCTION OF DIFFERENT METHODS
FOR SOLVING OF NONLINEAR PROBLEMS OF THE CONSTRAINED OPTIMIZATION
For the numerical solution of smooth problems of the constrained optimization with nonlinear restrictions in inequalities
form the general scheme of approximating methods of sequential square programming is worked out on the basis of
relaxation of penalty function containing smooth and nonsmooth penalties. By means of this scheme the methods of
nonsmooth penalties are described.
A.A. Belousov
IMPULSE CONTROLS IN DIFFERENTIAL GAMES UNDER INTEGRAL CONSTRAINS
Linear systems under general convex integral constraints on controls are discussed in this paper. It is proposed the
generalization of differential games by means of impulse controls. Analog of Pontryagin’s Condition is formulated. On its
basis sufficient conditions of the game termination in a certain guaranteed time are obtained.
G.D. Bila, A.P. Knopov
ON A CLASS OF PERIODOGRAM ESTIMATES
We proposed a class of periodogram estimates of unknown parameters of the nonlinear regression model «signal plus
noise». We proved their strong consistency provided that the regression function is almost periodic and the noise is a
functional of a random Gaussian process with long-range dependence.
K.G. Dziubenko
FUNCTION SECOND VARIATION AND CONVERGENCE IN NORM
In bounded second variation functions space statements are proved on convergence and variations calculation, norms and
scalar product are introduced.
V.B. Pavlenko
SOFTWARE IMPLEMENTATION FOR SYSTEMS OF EQUATIONS IN THE CLASS OF RESIDUES MODULO 3
The article proposes an approach that can be useful in solving the problem of coloring planar graphs with four colors.
A.V. Popov
ON THE EFFICIENT METHOD FOR THE SOLVING OF INCORRECT PROBLEMS
WITH SPARSE MATRICES
A three-staged regularization method is proposed for the finding within a priori given accuracy of approximations either to
normal generalized or weighted normal generalized solutions of linear algebraic system with positive semi-defined sparse
symmetric matrix.
D.A. Gololobov
CONSISTENCY OF ESTIMATION OF THE UNKNOWN PARAMETER FOR GOMOGENOUS RANDOM FIELD
WITH CONTINUOUS TIME
Empirical estimation of unknown parameter for two-dimensional random field with strong mixing is considered.
Conditions, under which strong consistency of this estimation holds, are established.
V.I. Biletsky, G.A. Donets, E.I. Nenakhov
ONE PROBLEMS OF UNLIMITED COMBINATORIAL RECOGNITION
The problem, concerping unlimited combinatorial problems of recognition, is analyzed. With the help of minimal amount
of tests it is necessary to detect 2 radioactive balls from a set of balls. A number of assertions is proved, necessary to
construct an optimal strategy. The problem solutions are provided in the cases of 15 and 22 balls.
Yu.P. Laptin
USING PENALTY FUNCTIONS FOR SOLVING SOME OPTIMIZATION PROBLEMS
There are considered the problems of use of exact penalty functions for solving optimization problems with constraints.
The approaches are proposed that allow to determine the coefficients of penalty in the course of an optimization algorithm.
Sufficient conditions are formulated under which the solution of the auxiliary problem is the solution of the original
problem.
O.P. Lykhovyd, A.V. Fesyuk, A.V. Ivlichev
OPTIMAL LOAD OF POWER SYSTEM WITH UNITS DISABLING
The problem of finding optimal load of power system with units disabling and with account of «environmental»
constraints is considered. A mathematical model of the problem, the implementation in AMPL modeling language and test
results on NEOS server by Gurobi program are given.
V.A. Zhydkov
CALCULATION OF MULTILAYER OPTICAL COATING USING RECOURSIVE LAYER STRUCTURE
This article presents an empirical algorithm for optical coating optimization procedure, using recursive layer structure.
There are results, demonstrating that in a number of cases, it can significantly improve optimization procedure efficiency
by decreasing number of parameters to be optimized on every step of the procedure suggested.
V.V. Boyko, V.V. Gorin, V.M. Kuzmenko
INFORMATION DISPERSAL ALGORITHM OPTIMIZATION IN A DISTRIBUTED STORAGE SYSTEM
The problem of information dispersal algorithm optimization in distributed data storage is discussed. Necessary security,
reliability and confidentiality requirements are claimed. Testing results for algorithms proposed provided.
N.G. Zhurbenko, B.M. Chumakov
ON ONE MODEL OF MULTICOMMODITY TRANSPORTATION PROBLEM
The article describes mathematical model and solution method for a class of transportation on transport network problem.
The solution method utilises nonsmooth optimization algorithm. The approximate solution algorithm of the problem with
account of discrete constraints is proposed.
Aghaei Agh Ghamish Yaghoub, G.A. Donets
THE TASK ABOUT THE MATHEMATICAL SAFE ON MATRICES
The task about the mathematical safe, set on a matrix is considered. The safe with the same type of locks is researched. We
have found the necessary conditions of the solution of the task for a prime number of states of the lock.
V.M. Gorbachuk, G.O. Shulinok
OPTIMAL SOCIAL WELFARE ON THE MARKET OF GASOLINES
The universal approach to social welfare optimization of a sector with factor supply, production, demand on final
products.
T.A. Lazebna
MODELLING OF RADIONUCLIDES INFLUENCE
ON IMMUNE SYSTEM PARAMETRES
The definition problem of the most informative parametres of an organism immune system under influence of small
ionising radiation doses are investigated. Mathematical modelling of radionuclides influence on the humoral immune
response of an organism are discussed. Numerical results of dynamic problems are presented.
Е.І. Nenakhov, Т.Е. Romanova, P.І. Stetsyuk
BALANCED PACKING PROBLEM OF CIRCLES IN A CIRCLE OF MINIMUM RADIUS
The paper considers a packing problem of a set of unequal circles into a containing circle of the minimum radius subject
to the center of gravity of the set of circles is located at the center of the containing circle. We introduce two formulations
of the packing problem: in the form of a quadratic extremal problem and, as well as, in the form of inverse-convex
programming. We employ a method based on the modification of the r -algorithm for local optimization. The results of
computational experiments are given.
J.I. Bihun, E.A. Liubarshchuk
ON COLLISION AVOIDANCE IN THE GAME PROBLEM OF GROUP INTERACTION
The problem of escaping of at least one evaders is analysed in the case of interaction of four pursuers and two evaders,
having “simple motion” dynamics and control domains in the form of unit spheres. It is shown that at least one of the
evaders can escape. The corresponding motion control is program designed and computer simulated.