In the framework of control parameterization method the optimization problem with respect to linear phase system with quadratic functional is considered. Approximation of the control is obtained in the class of piecewise constant functions. It is formed as a linear combination of a special set of support functions. Coefficients of this combination are variables of the finite-dimensional problem. To effectively solve this problem explicit expressions for the functional with respect to parameters of approximations are obtained. As a result the quadratic mathematical programming problem is formulated.
Optimal control problem without phase and terminal constraints is considered. Conceptions of strongly extremal controls are introduced on the basis of nonstandard functional increment formulas. Such controls are optimal in linear and quadratic problems. In general case optimality property is guaranteed by concavity condition of the Pontryagin function with respect to phase variables. 2010 Mathematics Subject Classification. 49K15.
One of the priorities of the Russian state is the effective financing of the regional economy. Not always directed financial flows have the expected effect, which would generate stable development of the regional economy. The conducted research shows that a unified approach to financing regions does not represent the best strategy aimed at the development of the subjects of the Russian Federation as a whole. Nowadays, in terms of further development, the Siberian Federal District comes out on top, since a sufficiently large variety of areas of development of the country directly relates to it. Based on this, the authors have studies the regions of this district, analyzing various socio-economic factors that affect the gross regional product. The constructed factor models reflecting the interrelation of factors influencing the growth of the gross regional product aid in dividing the regions into three clusters that differ significantly from each other. The authors have used the data for 2000-2019 when accurately assessing the characteristics of each region. Characterizing the constructed clusters has required a special terminology: region-society, region-quasi-state and region-quasi-corporation. Such structure helped in determining the way of the regions’ rational financing in order to achieve the greatest efficiency of development. Based on the conducted research, one can build not only an optimal financing strategy for each subject of the Russian Federation, but also to determine the financial policy of the country. That in turn will improve both the socio-economic indicators of the regions and the quality of life of the population of our entire country.
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