Geodesic
On Optimal Harvesting of a Resource on a Circle
Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 565-578 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper studies the optimality in the problem of cyclic harvesting of a resource distributed on a circle with a certain prescribed density. The velocity of motion of the collecting device and the fraction of the resource harvested at a given time play the role of control. The problem is to choose a control maximizing a given quality functional. The paper presents the maximum principle for this (infinite-dimensional) problem. The maximum principle can be written as two inequalities which can be conveniently verified. The class of problems with a concave profit function is solved completely. At the end of the paper, several examples are considered to illustrate the developed technique.
Keywords: cyclic harvesting of a resource, maximum principle, spatially distributed resource, necessary conditions for optimality. 
@article{MZM_2017_102_4_a8,
     author = {M. I. Zelikin and L. V. Lokoutsievskiy and S. V. Skopintcev},
     title = {On {Optimal} {Harvesting} of a {Resource} on a {Circle}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {565--578},
     year = {2017},
     volume = {102},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a8/}
}
TY  - JOUR
AU  - M. I. Zelikin
AU  - L. V. Lokoutsievskiy
AU  - S. V. Skopintcev
TI  - On Optimal Harvesting of a Resource on a Circle
JO  - Matematičeskie zametki
PY  - 2017
SP  - 565
EP  - 578
VL  - 102
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a8/
LA  - ru
ID  - MZM_2017_102_4_a8
ER  - 
%0 Journal Article
%A M. I. Zelikin
%A L. V. Lokoutsievskiy
%A S. V. Skopintcev
%T On Optimal Harvesting of a Resource on a Circle
%J Matematičeskie zametki
%D 2017
%P 565-578
%V 102
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a8/
%G ru
%F MZM_2017_102_4_a8
M. I. Zelikin; L. V. Lokoutsievskiy; S. V. Skopintcev. On Optimal Harvesting of a Resource on a Circle. Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 565-578. http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a8/

[1] H. S. Gordon, “Economic theory of a common property resource: the fishery”, J. Polit. Economy, 62:2 (1954), 124–142 | DOI

[2] A. D. Scott, “The fishery: The objectives of sole ownership”, J. Polit. Economy, 63:2 (1955), 116–124 | DOI

[3] L. V. Lokutsievskii, “Optimalnyi veroyatnostnyi poisk”, Matem. sb., 202:5 (2011), 77–100 | DOI | MR | Zbl

[4] S. Behringer, T. Upmann, “Optimal harvesting of a spatial renewable resource”, J. Econom. Dynam. Control, 42 (2014), 105–120 | DOI | MR

[5] A. O. Belyakov, A. A. Davydov, V. M. Veliov, “Optimal cyclic exploitation of renewable resources”, J. Dyn. Control Syst., 21:3 (2015), 475–494 | DOI | MR | Zbl

[6] V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Optimalnoe upravlenie, Fizmatlit, M., 2005 | MR | Zbl