Mathematical model of financing the education system in the form of optimal control problem and its application

The purpose of the article is to develop a general methodology for calculating the optimal financing of the education system. To achieve this goal, methods of optimal discrete processes theory were used: model was built where the number of students at various levels of education was considered as phase variables, and budget expenditures by items were considered as control parameters. Algorithm for solving the problem of the optimal distribution of expenditures is formulated, which is applied on the example of both the Russian Federation as a whole and at the level of a separate region - the Novosibirsk region. The items of expenditure of the federal and regional budgets are identified, in which it is recommended to make adjustments.