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Constant Versus Periodic Fishing: Age Structured Optimal Control Approach

Published online by Cambridge University Press:  20 June 2014

A.O. Belyakov  and
V.M. Veliov
A.O. Belyakov*
Affiliation:
ORCOS, Vienna University of Technology Institute of Mechanics, Lomonosov Moscow State University
V.M. Veliov
Affiliation:
ORCOS, Vienna University of Technology
*
⋆ Corresponding author. E-mail: anton.belyakov@tuwien.ac.at
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Abstract

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.

Keywords

age-structured systemsperiodic controloptimal fishingproperness test
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 4: Optimal control , 2014 , pp. 20 - 37
Copyright
© EDP Sciences, 2014

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References

Aniţa, L.-I., Aniţa, S., Arnǎutu, V.. Global behavior for an age-dependent population model with logistic term and periodic vital rates. Applied Mathematics and Computation, 206 (2008), No. 1, 368–379. CrossRefGoogle Scholar
S. Aniţa. Analysis and Control of Age-Dependent Population Dynamics, Mathematical Modelling Series. Springer, 2000.
Aniţa, L.-I. Aniţa, S., Arnǎutu, V.. Optimal harvesting for periodic age-dependent population dynamics with logistic term. Applied Mathematics and Computation, 215 (2009), 2701–2715. CrossRefGoogle Scholar
Aniţa, S., Arnǎutu, V., Ştefǎnescu, R.. Numerical optimal harvesting for a periodic age-structured population dynamics with logistic term. Numerical Functional Analysis and Optimization, 30 (2009), No. 3–4, 183–198. CrossRefGoogle Scholar
Aragon, F.J., Dontchev, A.L., Gaydu, M., Geoffroy, M.H., Veliov, V.M.. Metric Regularity of Newton’s Iteration. SIAM Journal on Control and Optimization, 49 (2011), No. 2, 339–362. Google Scholar
C. W. Clark. Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Wiley, New York, l976.
Colonius, F., Kliemann, W.. Infinite time optimal control and periodicity, Applied Mathematics and Optimization. 20 (1989), No. 1, 113–130. Google Scholar
A.L. Dontchev, R.T. Rockafellar. Implicit Functions and Solution Mappings. Springer Mathematics Monographs, Springer, Dordrecht, 2009.
Dontchev, A.L., Veliov, V.M.. Metric Regularity under Approximations. Control & Cybernetics, (2009), 38/4B, No. 4, 1283–1303. Google Scholar
Feichtinger, G., Tragler, G., Veliov, V.M.. Optimality conditions for age-structured control systems. J. Math. Anal. Appl., 288, (2003), No. 1, 47–68. CrossRefGoogle Scholar
Hartl, R. F., On the properness of one-dimensional periodic control problems. Systems & Control Letters, 20 (1993), No. 5, 393–395. CrossRefGoogle Scholar
M. Iannelli. Mathematical theory of age-structured population dynamics, Applied mathematics monographs. C.N.R., Giardini editori e stampatori, Pisa, 1995.
O. Tahvonen. Age-sructured optimization models in fisheries bioeconomics, Taylor and Francis, (2011), 140–173.
H. Thieme, Mathematics in Population Biology, Mathematical Biology Series, Princeton University Press, 2003.
G. F. Webb. Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, New York, 1985.