Geodesic
On necessary optimality conditions for Ramsey-type problems
Ural mathematical journal, Tome 5 (2019) no. 1, pp. 24-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study an optimal control problem in infinite time, where the integrand does not depend explicitly on the state variable. A special case of such problem is the Ramsey optimal capital accumulation in centralized economy. To complete the optimality conditions of Pontryagin’s maximum principle, so called transversality conditions of different types are used in the literature. Here, instead of a transversality condition, an additional maximum condition is considered.
Keywords: Pontryagin maximum principle, transversality condition, optimal control, Ramsey problem. 
@article{UMJ_2019_5_1_a2,
     author = {Anton O. Belyakov},
     title = {On necessary optimality conditions for {Ramsey-type} problems},
     journal = {Ural mathematical journal},
     pages = {24--30},
     year = {2019},
     volume = {5},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a2/}
}
TY  - JOUR
AU  - Anton O. Belyakov
TI  - On necessary optimality conditions for Ramsey-type problems
JO  - Ural mathematical journal
PY  - 2019
SP  - 24
EP  - 30
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a2/
LA  - en
ID  - UMJ_2019_5_1_a2
ER  - 
%0 Journal Article
%A Anton O. Belyakov
%T On necessary optimality conditions for Ramsey-type problems
%J Ural mathematical journal
%D 2019
%P 24-30
%V 5
%N 1
%U http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a2/
%G en
%F UMJ_2019_5_1_a2
Anton O. Belyakov. On necessary optimality conditions for Ramsey-type problems. Ural mathematical journal, Tome 5 (2019) no. 1, pp. 24-30. http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a2/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F., The Mathematical Theory of Optimal Processes, Pergamon, Oxford, NY, 1964, 338 pp. | MR | Zbl

[2] Cass D., “Optimum growth in an aggregative model of capital accumulation”, Rev. Econom. Stud., 32:3 (1965), 233–240 | DOI | MR

[3] Ramsey F. P., “A mathematical theory of saving”, The Economic J., 38:152 (1928), 543–559 | DOI

[4] Romer D., Advanced Macroeconomics, 4-th ed., McGraw-Hill, NY, 2012, 736 pp.

[5] Carlson D. A., Haurie A. B., Leizarowitz A., Infinite Horizon Optimal Control, Springer-Verlag, Berlin-Heidelberg, 1991, 332 pp. | DOI | MR | Zbl

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

[7] Shell K., “Applications of Pontryagin's maximum principle to economics”, Mathematical Systems Theory and Economics I/II, 11–12 (1969), 241–292 | MR

[8] Kamihigashi T., “Necessity of transversality conditions for infinite horizon problems”, Econometrica, 69:4 (2001), 995–1012 | DOI | MR | Zbl

[9] Michel P., “On the transversality condition in infinite horizon optimal problems”, Econometrica, 50:4 (1982), 975–985 | DOI | MR | Zbl

[10] Aseev S., Veliov V., “Maximum principle for infinite-horizon optimal control problems with dominating discount”, Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications Algorithms, 19:1–2 (2012), 43–63 http://pure.iiasa.ac.at/9874 | MR | Zbl

[11] Aseev S., Veliov V., “Needle variations in infinite-horizon optimal control”, Contemp. Math., 619 (2014), 1–17 | DOI | MR | Zbl

[12] Aseev S. M., Besov K. O., Kryazhimskii A. V., “Infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 67:2 (2012), 195–253 | DOI | MR | Zbl

[13] Aseev S. M., Kryazhimskiy A. V., “The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons”, SIAM J. Control Optim., 43:3 (2004), 1094–1119 | DOI | MR | Zbl

[14] Aseev S. M., Veliov V. M., “Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions”, Proc. Steklov Inst. Math., 291:1 (2015), 22–39 | DOI | MR

[15] Khlopin D., “Necessity of vanishing shadow price in infinite horizon control problems”, J. Dyn. Control Syst., 19:4 (2013), 519–552 | DOI | MR | Zbl

[16] Khlopin D., “Necessity of limiting co-state arcs in Bolza-type infinite horizon problem”, Optimization, 64:11 (2015), 2417–2440 | DOI | MR | Zbl

[17] Belyakov A. O., Necessary Conditions for Infinite Horizon Optimal Control Problems Revisited, 2017, arXiv: : 1512.01206v2 [math.OC]