Geodesic
The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval
Informatics and Automation, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 71-88.

Voir la notice de l'article provenant de la source Math-Net.Ru

A class of nonlinear optimal control problems with infinite time interval is investigated that arise in mathematical economics. Necessary conditions of optimality in the form of the Pontryagin maximum principle are obtained that contain additional conditions on the adjoint function and on the behavior of the Hamiltonian at infinity. In some cases, these additional conditions guarantee the validity of the usual transversality conditions at infinity. 
@article{TRSPY_2001_233_a1,
     author = {S. M. Aseev and A. V. Kryazhimskii and A. M. Tarasyev},
     title = {The {Pontryagin} {Maximum} {Principle} and {Transversality} {Conditions} for an {Optimal} {Control} {Problem} with {Infinite} {Time} {Interval}},
     journal = {Informatics and Automation},
     pages = {71--88},
     publisher = {mathdoc},
     volume = {233},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2001_233_a1/}
}
TY  - JOUR
AU  - S. M. Aseev
AU  - A. V. Kryazhimskii
AU  - A. M. Tarasyev
TI  - The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval
JO  - Informatics and Automation
PY  - 2001
SP  - 71
EP  - 88
VL  - 233
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2001_233_a1/
LA  - ru
ID  - TRSPY_2001_233_a1
ER  - 
%0 Journal Article
%A S. M. Aseev
%A A. V. Kryazhimskii
%A A. M. Tarasyev
%T The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval
%J Informatics and Automation
%D 2001
%P 71-88
%V 233
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2001_233_a1/
%G ru
%F TRSPY_2001_233_a1
S. M. Aseev; A. V. Kryazhimskii; A. M. Tarasyev. The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval. Informatics and Automation, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 71-88. http://geodesic.mathdoc.fr/item/TRSPY_2001_233_a1/

[1] Arutyunov A. V., “Vozmuscheniya ekstremalnykh zadach s ogranicheniyami i neobkhodimye usloviya optimalnosti”, Itogi nauki i tekhniki. Matematicheskii analiz, 27, VINITI, M., 1989, 147–235 | MR

[2] Arutyunov A. V., Aseev S. M., “Printsip maksimuma v zadachakh optimalnogo upravleniya s fazovymi ogranicheniyami. Nevyrozhdennost i ustoichivost”, Dokl. RAN, 334:2 (1994), 134–137 | MR | Zbl

[3] Arutyunov A. V., Aseev S. M., Blagodatskikh V. I., “Neobkhodimye usloviya pervogo poryadka v zadache optimalnogo upravleniya differentsialnym vklyucheniem s fazovymi ogranicheniyami”, Mat. sb., 184:6 (1993), 3–32 | MR | Zbl

[4] Aseev S. M., “Metod gladkikh approksimatsii v teorii neobkhodimykh uslovii optimalnosti dlya differentsialnykh vklyuchenii”, Izv. RAN. Ser. mat., 61:2 (1997), 3–26 | MR | Zbl

[5] Mordukhovich B. Sh., Metody approksimatsii v zadachakh optimizatsii i upravleniya, Nauka, M., 1988 | MR | Zbl

[6] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1969

[7] Filippov A. F., “O nekotorykh voprosakh teorii optimalnogo regulirovaniya”, Vestn. MGU. Matematika. Mekhanika. Astronomiya. Fizika. Khimiya, 1959, no. 2, 25–32 | MR | Zbl

[8] Arrow K., “Application of control theory to economic growth”, Mathematics of the decision sciences, Pt. 2, Lect. Appl. Math., 12, Amer. Math. Soc., Providence, RI, 1968, 83–119 | MR

[9] Arrow K., Kurz M., Public investment, the rate of return, and optimal fiscal policy, J. Hopkins Press, Baltimore, London, 1970

[10] Arutyunov A. V., Aseev S. M., “Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints”, SIAM J. Contr. and Optim., 35:3 (1997), 930–952 | DOI | MR | Zbl

[11] Aseev S. M., “Methods of regularization in nonsmooth problems of dynamic optimization”, J. Math. Sci., 94:3 (1999), 1366–1393 | DOI | MR | Zbl

[12] Aubin J. P., Clarke F. H., “Shadow prices and duality for a class of optimal control problems”, SIAM J. Contr. and Optim., 17:5 (1979), 567–586 | DOI | MR | Zbl

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

[14] Cesari L., Optimization — theory and applications: Problems with ordinary differential equations, Springer, Berlin etc., 1983 | MR

[15] Dolcetta I. C., “On a discrete approximation of the Hamilton–Jacobi equation of dynamic programming”, Appl. Math. and Optim., 10 (1983), 367–377 | DOI | MR

[16] Grossman G. M., Helpman E., Innovation and growth in the global economy, MIT Press, Cambridge, MA, 1991

[17] Halkin H., “Necessary conditions for optimal control problems with infinite horizons”, Econometrica, 42:2 (1974), 267–272 | DOI | MR | Zbl

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

[19] Mangasarian O. L., “Sufficient conditions for the optimal control of nonlinear systems”, SIAM J. Contr., 4:1 (1966), 139–152 | DOI | MR | Zbl

[20] Skiba A. K., “Optimal growth with convex-concave production function”, Econometrica, 46:3 (1978), 527–539 | DOI | MR | Zbl

[21] Tarasyev A., Watanabe C., Optimal control of RD investment in a techno-metabolic system, IIASA Interim Report, 1999. IR-1999-001

[22] Tarasyev A., Watanabe C., “Optimal dynamics of innovation in models of economic growth”, J. Optim. Theory and Appl., 108:1 (2001), 175–203 | DOI | MR | Zbl