MODELLING OF OPTIMAL CONTROL PROBLEMS IN MATHEMATICAL ECONOMICS ON BASE OF TOPOLOGICAL METHODS

Abstract

The work is devoted to the application of the general topology conception for development of the mathematical tooling for analysis of some class of the optimization models in the mathematical economics. This class includes the optimization models in which only some vector components of the control render the action on the phase variables in each time moment. For analysis of the simular models, the modification of classical A.Ya. Dubovitsky and A.A. Milutin scheme for analysis of the first order necessary extremum conditions with use of the topological compendency concept has been developed. It has been proved that in this case in extremum point either the non-trivial solution of the Euler equation exists or some inclusion for cones from conjugated space is performed. This result represents the important achievement in the theory of non-differentiated optimization. On its base the concretization of the maximum principle for the specified class of the mathematical economics models has been obtained. It has been shown that in the space with measure the more strong necessary sonditions can be obtained with using the introduced of the informative functional.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio