Geodesic
Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems
Informatics and Automation, Optimal control, Tome 262 (2008), pp. 127-145 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider an optimal control problem with a functional defined by an improper integral. We study the concavity properties of the maximized Hamiltonian and analyze the Hamiltonian systems in the Pontryagin maximum principle. On the basis of this analysis, we propose an algorithm for constructing an optimal trajectory by gluing the dynamics of the Hamiltonian systems. The algorithm is illustrated by calculating an optimal economic growth trajectory for macroeconomic data. 
@article{TRSPY_2008_262_a9,
     author = {A. A. Krasovskii and A. M. Tarasyev},
     title = {Properties of {Hamiltonian} {Systems} in the {Pontryagin} {Maximum} {Principle} for {Economic} {Growth} {Problems}},
     journal = {Informatics and Automation},
     pages = {127--145},
     year = {2008},
     volume = {262},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a9/}
}
TY  - JOUR
AU  - A. A. Krasovskii
AU  - A. M. Tarasyev
TI  - Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems
JO  - Informatics and Automation
PY  - 2008
SP  - 127
EP  - 145
VL  - 262
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a9/
LA  - ru
ID  - TRSPY_2008_262_a9
ER  - 
%0 Journal Article
%A A. A. Krasovskii
%A A. M. Tarasyev
%T Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems
%J Informatics and Automation
%D 2008
%P 127-145
%V 262
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a9/
%G ru
%F TRSPY_2008_262_a9
A. A. Krasovskii; A. M. Tarasyev. Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems. Informatics and Automation, Optimal control, Tome 262 (2008), pp. 127-145. http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a9/

[1] Intriligator M., Matematicheskie metody optimizatsii i ekonomicheskaya teoriya, Airis-press, M., 2002

[2] Arrow K. J., “Applications of control theory to economic growth”, Mathematics of the decision sciences, Part 2, Amer. Math. Soc., Providence, RI, 1968, 85–119 | MR

[3] Ayres R. U., Warr B., “Accounting for growth: The role of physical work”, Structural Change and Economic Dynamics, 16:2 (2005), 181–209 | DOI

[4] Solow R. M., Growth theory: an exposition, Oxford Univ. Press, New York, 1970

[5] Shell K., “Applications of Pontryagin's maximum principle to economics”, Mathematical systems theory and economics, V. 1, Springer, Berlin, 1969, 241–292 | MR

[6] Tarasyev A. M., Watanabe C., “Dynamic optimality principles and sensitivity analysis in models of economic growth”, Nonlin. Anal. Theory, Meth. and Appl., 47:4 (2001), 2309–2320 | DOI | MR | Zbl

[7] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976 | Zbl

[8] Aseev S. M., Kryazhimskii A. V., Printsip maksimuma Pontryagina i zadachi optimalnogo ekonomicheskogo rosta, Tr. MIAN, 257, Nauka, M., 2007 | MR

[9] Rokafellar R. T., Vypuklyi analiz, Mir, M., 1973

[10] Hartman Ph., Ordinary differential equations, J. Wiley and Sons, New York–London–Sydney, 1964 | MR | Zbl

[11] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR | Zbl

[12] Balder E. J., “An existence result for optimal economic growth problems”, J. Math. Anal. and Appl., 95 (1983), 195–213 | DOI | MR | Zbl