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

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.

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Acknowledgements

This work was supported by the German Science Foundation (DFG) through the Excellence Cluster Future Ocean by project number CP 1336. This support is gratefully acknowledged.

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Correspondence to Malte Braack.

Additional information

Communicated by Stefan Ulbrich.

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Braack, M., Quaas, M.F., Tews, B. et al. Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem. J Optim Theory Appl 178, 950–972 (2018). https://doi.org/10.1007/s10957-018-1304-7

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Keywords

  • Fishing strategies
  • Optimal control
  • Non-convex optimization

Mathematics Subject Classification

  • 35K20
  • 35K45
  • 35K57
  • 49K20
  • 49K40
  • 65M60