МАТЕМАТИЧЕСКАЯ СОСТАВЛЯЮЩАЯ ОПТИМАЛЬНОГО УПРАВЛЕНИЯ

Abstract

The possibilities of using mathematical tools to find the optimal solution to a formalized economic (control) problem are analyzed depending on the chosen optimization criterion and taking into account restrictions on the controlled parameters. It is noted that tasks that are completely different in terms of their goals, from the point of view of mathematics, assume a fairly standard solution scheme, the first stage of which consists in formalizing the problem and discussing the existence and uniqueness of the solution. We are talking not only about the problem of finding the best solution, but also about the possibility of forecasting in order to change the control parameters. It is shown how the optimization problem is reduced to finding the extremum of the objective function or even the objective functional. If there are no restrictions during formalization, then this will be the problem of finding an unconditional extremum; if the restrictions are given by a system of equalities, then this will be the problem of finding a conditional extremum; if the restrictions are given by a system of inequalities, then this will be the problem of finding a global extremum. The described mathematical toolkit is considered in more detail for two important problems of the economy – optimal resource management and optimal distribution of investments.