Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
40
12
2008
On Scalarization of a Class of Vector Optimization Problems in the Banach Spaces
1-13
Igor V.
Nechay
Dnepropetrovsk National University of Railway Transport, Ukraine
Peter I.
Kogut
Oles Honchar Dnepropetrovsk National University
We consider a class of problems of nonscalar optimization in the Banach spaces, which indexes of quality is not obligatory lower semicontinuous mapping. Solvability conditions for these problems are given and it is shown that certain part of the set of solutions can be obtained as a result of scalarization procedure. Illustrative examples are shown.
The Necessary Optimality Conditions for Continuous Problems of Set Partitioning in Terms of the Theory of Set Functions
14-26
Alexandra A.
Zhiltsova
Oles Honchar Dnepropetrovsk National University
Elena M.
Kiseleva
Oles Honchar Dnipro National University, Dnepr
The necessary conditions of the optimality for continuous problems of optimal set partitioning with the restrictions in the form of inequalities are formulated in a general form and proved in terms of the theory of set functions. The obtained necessary conditions are specified for the linear continuous problem of optimal set partitioning without centers arrangement.
Solution and Investigation of Vector Problems of Combinatorial Optimization on a Set of Polypermutations
27-42
Natalya V.
Semenova
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Lyudmila N.
Kolechkina
University of Lodz, Lodz (Poland)
Alla N.
Nagornaya
National University of "Kyiv-Mohyla
Academy", Kiev
We investigated complicated vector problems on combinatorial set of polypermutations. Some properties of accessible region of the combinatorial multicriterion problem, which is solved in arithmetic Euclidian space, were studied. We obtained necessary and sufficient conditions of optimality of different types of efficient solutions. The method for search of Pareto-optimal solutions of the considered class of problems was constructed.
Relation of Differential Rotation of Magnetic Fields on the Sun with Sign and Magnitude of Field Intensity
43-60
Yarema I.
Zyelyk
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Kyiv, Ukraine
Nataliya N.
Stepanyan
Research Institute "Crimean Astrophysical Observatory" of Ministry of Education and Science of Ukraine, Crimea, settlement Nauchnyi of Bakhchisaraiskiy region
Olga A.
Andryeyeva
Research Institute "Crimean Astrophysical Observatory" of Ministry of Education and Science of Ukraine, Crimea, settlement Nauchnyi of Bakhchisaraiskiy region
By using spectrum analysis for evaluation of stationary differential rotation of magnetic fields on the Sun on the basis of obtained dependencies of statistically significant periods of rotation on latitude according to observations on an interval, which covers three last cycles of activity in the range of modulus of magnetic field intensity [0; 700) Gs we detect two classes of magnetic fields similar by characteristic of rotation, i.e.. weak ones [0; 50) Gs and stronger ones [50, 700) Gs. Distinctive features of two detected classes of magnetic fields on the Sun are supplemented with differences in degree of differential rotation besides such characteristics as cycle duration and unbalance of fields of N- and S-polarities.
The Cartel Optimum and the Reasonable Cournot−Nash Equilibrium for Fractional Objective Functions
61-70
Vasiliy M.
Gorbachuk
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
For fractional objective functions the criterion that the classic Cournot−Nash equilibrium gives the profitability below 100 % is found, and in that case it is suggested to consider the reasonable Cournot−Nash equilibrium. The latter is a projection of the classic equilibrium on the constructed set. For fractional objective functions the production of a firm in the Cournot−Nash equilibrium exceeds the production of a firm in the cartel optimum, but the proportion of the corresponding profits is ambiguous.
Contents
71-82