Abstract
The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.
Similar content being viewed by others
References
V. K. Bulgakov and V. V. Strigunov, Preprint No. 96, VTs DVO RAN (Computing Center, Far East Division, Russian Academy of Sciences, Khabarovsk, 2006).
V. K. Bulgakov and O. V. Bulgakov, “Modeling the Dynamics of Generalizing Development Indices for Regional Economic System of Russia,” Ekon. Mat. Metody 42(1), 32–49 (2006).
L. S. Pontryagin, et. al., Mathematical Theory of Optimal Processes (Nauka, Moscow, 1976) [in Russian].
L. S. Pontryagin, Selected Scientific Works: Vol. II (Nauka, Moscow, 1988) [in Russian].
Yu. A. Dubinskii, “Quasilinear Elliptic and Parabolic Equations of Arbitrary Order,” Usp. Mat. Nauk 23(1), 45–90 (1968).
L. S. Pontryagin, Ordinary Differential Equations (Addison-Wesley, Reading, Mass., 1962; Nauka, Moscow, 1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.K. Bulgakov, V.V. Strigunov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 5, pp. 776–790.
Rights and permissions
About this article
Cite this article
Bulgakov, V.K., Strigunov, V.V. Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle. Comput. Math. and Math. Phys. 49, 748–761 (2009). https://doi.org/10.1134/S0965542509050029
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542509050029