Geodesic
Boundary value problem of Pontryagin's maximum principle in a two-sector economy model with an integral utility function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1812-1826 
Yu. N. Kiselev; M. V. Orlov; S. M. Orlov. Boundary value problem of Pontryagin's maximum principle in a two-sector economy model with an integral utility function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1812-1826. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a1/
@article{ZVMMF_2015_55_11_a1,
     author = {Yu. N. Kiselev and M. V. Orlov and S. M. Orlov},
     title = {Boundary value problem of {Pontryagin's} maximum principle in a two-sector economy model with an integral utility function},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1812--1826},
     year = {2015},
     volume = {55},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a1/}
}
TY  - JOUR
AU  - Yu. N. Kiselev
AU  - M. V. Orlov
AU  - S. M. Orlov
TI  - Boundary value problem of Pontryagin's maximum principle in a two-sector economy model with an integral utility function
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1812
EP  - 1826
VL  - 55
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a1/
LA  - ru
ID  - ZVMMF_2015_55_11_a1
ER  - 
%0 Journal Article
%A Yu. N. Kiselev
%A M. V. Orlov
%A S. M. Orlov
%T Boundary value problem of Pontryagin's maximum principle in a two-sector economy model with an integral utility function
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1812-1826
%V 55
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a1/
%G ru
%F ZVMMF_2015_55_11_a1

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

An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin's maximum principle yields a boundary value problem with special conditions at infinity. The search for the solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal solution. In the construction of the solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the extremal solution obtained by applying the maximum-principle boundary value problem.

[1] Kiselev Yu. N., Orlov M. V., “Issledovanie odnoi dvukhsektornoi modeli ekonomicheskogo rosta s proizvodstvennoi funktsiei Kobba–Duglasa”, Vestn. Mosk. un-ta. Ser. 15. Vychisl. matem. i kibern., 2010, no. 2, 56–63 | MR

[2] Kiselev Yu. N., Orlov M. V., “Optimalnaya programma raspredeleniya resursov v dvukhsektornoi ekonomicheskoi modeli s proizvodstvennoi funktsiei Kobba–Duglasa”, Differents. ur-niya, 46:12 (2010), 1749–1765 | MR | Zbl

[3] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1961

[4] Iwasa Y., Roughgarden J., “Shoot/root balance of plants: optimal growth of a system with many vegitative organs”, Theoretical Population Biology, 25 (1984), 78–105 | DOI | MR | Zbl

[5] Kiselev Yu. N., Orlov M. V., “Optimalnaya programma raspredeleniya resursov v dvukhsektornoi ekonomicheskoi modeli s proizvodstvennoi funktsiei Kobba-Duglasa pri razlichnykh koeffitsientakh amortizatsii”, Differents. ur-niya, 48:12 (2012), 1642–1657 | Zbl

[6] Kiselev Yu. N., Orlov M. V., Orlov S. M., “Optimalnaya programma raspredeleniya resursov v dvukhsektornoi ekonomicheskoi modeli s funktsionalom integralnogo tipa pri razlichnykh koeffitsientakh amortizatsii”, Differents. ur-niya, 51:5 (2015), 671–687 | DOI | Zbl

[7] Belenkii V. Z., Optimizatsionnye modeli ekonomicheskoi dinamiki. Ponyatiinyi apparat. Odnomernye modeli, Nauka, M., 2007

[8] Kiselev Yu. N., “Dostatochnye usloviya optimalnosti v terminakh konstruktsii printsipa maksimuma Pontryagina”, Matematicheskie modeli v ekonomike i biologii, MAKS Press, M., 2003, 57–67 | MR