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Mat. Zametki, 2017, Volume 102, Issue 4, Pages 565–578 (Mi mz11310)  

On Optimal Harvesting of a Resource on a Circle

M. I. Zelikinab, L. V. Lokoutsievskiyab, S. V. Skopintcevc

a Lomonosov Moscow State University
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c State Budget Professional Educational Institution of Moscow "Vorobyovy Gory", Moscow

Abstract: 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.

DOI: https://doi.org/10.4213/mzm11310

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English version:
Mathematical Notes, 2017, 102:4, 521–532

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 07.07.2016
Revised: 23.01.2017

Citation: M. I. Zelikin, L. V. Lokoutsievskiy, S. V. Skopintcev, “On Optimal Harvesting of a Resource on a Circle”, Mat. Zametki, 102:4 (2017), 565–578; Math. Notes, 102:4 (2017), 521–532

Citation in format AMSBIB
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\pages 565--578
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