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Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem

Author

Listed:
  • Malte Braack

    (University of Kiel)

  • Martin F. Quaas

    (University of Kiel)

  • Benjamin Tews

    (P3 - Management Consulting and Engineering Solutions)

  • Boris Vexler

    (Technical University of Munich)

Abstract

The behavior of a fishing fleet and its impact onto the biomass of fish can be described by a nonlinear parabolic diffusion–reaction equation. Looking for an optimal fishing strategy leads to a non-convex optimal control problem with a bilinear control action. In this work, we present such an optimal control formulation, prove its well-posedness and derive first- and second-order optimality conditions. These results provide a basis for tailored finite element discretization as well as for Newton type optimization algorithms. First numerical test problems show typical features as so-called No-Take-Zones and maximal fishing quota (total allowable catches) as parts of an optimal fishing strategy.

Suggested Citation

  • Malte Braack & Martin F. Quaas & Benjamin Tews & Boris Vexler, 2018. "Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 950-972, September.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1304-7
    DOI: 10.1007/s10957-018-1304-7
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    References listed on IDEAS

    as
    1. Olaf Benedix & Boris Vexler, 2009. "A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints," Computational Optimization and Applications, Springer, vol. 44(1), pages 3-25, October.
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    4. Eduardo Casas & Fredi Tröltzsch, 2012. "A general theorem on error estimates with application to a quasilinear elliptic optimal control problem," Computational Optimization and Applications, Springer, vol. 53(1), pages 173-206, September.
    5. Daniel Pauly & Dirk Zeller, 2016. "Catch reconstructions reveal that global marine fisheries catches are higher than reported and declining," Nature Communications, Nature, vol. 7(1), pages 1-9, April.
    6. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
    7. Sanchirico, James N. & Wilen, James E., 2001. "A Bioeconomic Model of Marine Reserve Creation," Journal of Environmental Economics and Management, Elsevier, vol. 42(3), pages 257-276, November.
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