Geodesic
Constant Versus Periodic Fishing: Age Structured Optimal Control Approach
A.O. Belyakov1, 2 ; V.M. Veliov1
1 ORCOS, Vienna University of Technology
2 Institute of Mechanics, Lomonosov Moscow State University
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 4, pp. 20-37.

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The paper investigates an age-structured infinite-horizon optimal control model of harvesting a biological resource, interpreted as fish. Time and age are considered as continuum variables. The main result shows that in case of selective fishing, where only fish of prescribed sizes is harvested, it may be advantageous in the log run to implement a periodic fishing effort, rather than constant (the latter suggested by single-fish models that disregard the age-heterogeneity). Thus taking into account the age-structure of the fish may qualitatively change the theoretically optimal fishing mode. This result is obtained by developing a technique for reliable numerical verification of second order necessary optimality conditions for the considered problem. This technique could be useful for other optimal control problems of periodic age-structured systems.
DOI : 10.1051/mmnp/20149403

A.O. Belyakov 1, 2 ; V.M. Veliov 1

1 ORCOS, Vienna University of Technology
2 Institute of Mechanics, Lomonosov Moscow State University 
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A.O. Belyakov; V.M. Veliov. Constant Versus Periodic Fishing: Age Structured Optimal Control Approach. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 4, pp. 20-37. doi : 10.1051/mmnp/20149403. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149403/

[1] L.-I. Aniţa, S. Aniţa, V. Arnǎutu Applied Mathematics and Computation 2008 368 379

[2] S. Aniţa. Analysis and Control of Age-Dependent Population Dynamics, Mathematical Modelling Series. Springer, 2000.

[3] L.-I. Aniţa, S. Aniţa, V. Arnǎutu Applied Mathematics and Computation 2009 2701 2715

[4] S. Aniţa, V. Arnǎutu, R. Ştefǎnescu Numerical Functional Analysis and Optimization 2009 183 198

[5] F.J. Aragon, A.L. Dontchev, M. Gaydu, M.H. Geoffroy, V.M. Veliov SIAM Journal on Control and Optimization 2011 339 362

[6] C. W. Clark. Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Wiley, New York, l976.

[7] F. Colonius, W. Kliemann. Infinite time optimal control and periodicity, Applied Mathematics and Optimization. 20 (1989), No. 1, 113–130.

[8] A.L. Dontchev, R.T. Rockafellar. Implicit Functions and Solution Mappings. Springer Mathematics Monographs, Springer, Dordrecht, 2009.

[9] A.L. Dontchev, V.M. Veliov Control & Cybernetics 2009 1283 1303

[10] G. Feichtinger, G. Tragler, V.M. Veliov J. Math. Anal. Appl. 2003 47 68

[11] R. F. Hartl Systems & Control Letters 1993 393 395

[12] M. Iannelli. Mathematical theory of age-structured population dynamics, Applied mathematics monographs. C.N.R., Giardini editori e stampatori, Pisa, 1995.

[13] O. Tahvonen. Age-sructured optimization models in fisheries bioeconomics, Taylor and Francis, (2011), 140–173.

[14] H. Thieme, Mathematics in Population Biology, Mathematical Biology Series, Princeton University Press, 2003.

[15] G. F. Webb. Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, New York, 1985.

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