Geodesic
On Optimal Harvesting of a Resource on a Circle
Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 565-578

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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. 
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     title = {On {Optimal} {Harvesting} of a {Resource} on a {Circle}},
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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/