Optimality Conditions for Central Fields of Trajectories
Author(s):
Yevgeny Nikolayevich Orel
Financial University under the Government of the Russian Federation
Leningrad ave., 49
Moscow, 125993 (SSE-3)
Russian Federation
Data Analysis, decision-making and financial technology department
Professor of the Department "Mathematics"
Oryol-EN@list.ru
Olga E. Orel
Financial University under the Government of the Russian Federation
Leningrad ave., 49
Moscow, 125993 (SSE-3)
Russian Federation
Data Analysis, decision-making and financial technology department
Associate Professor of "the department Mathematics"
Olga_Orel72@mail.ru
Abstract:
By following the calculus of variations procedure for analyzing optimal control problems on global extremum we study the possibility
of imbedding extremal into a central field of trajectories.
All elements of this field start from a given point and once
cover the domain of the state space. In calculus of variations
for the central field of extremals one examines the Weierstrass condition.
If it is fulfilled then each extremal gives a global extremum.
In general case the field may contain not only extremals.
In this article we prove that a smooth central field of
trajectories is optimal if and only if it consists from Pontryagin’s extremals.
The example of economic application is considered, where
the central field of optimals is constructed.
Keywords
- central field of trajectories
- global extremum
- optimal control
- Pontryagin's extremal
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