Journal of Optimization Theory and Applications

, Volume 178, Issue 3, pp 950–972 | Cite as

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

  • Malte BraackEmail author
  • Martin F. Quaas
  • Benjamin Tews
  • Boris Vexler


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.


Fishing strategies Optimal control Non-convex optimization 

Mathematics Subject Classification

35K20 35K45 35K57 49K20 49K40 65M60 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Malte Braack
    • 1
    Email author
  • Martin F. Quaas
    • 2
  • Benjamin Tews
    • 3
  • Boris Vexler
    • 4
  1. 1.Mathematical SeminarUniversity of KielKielGermany
  2. 2.Faculty of Business, Economics and Social SciencesUniversity of KielKielGermany
  3. 3.P3 - Management Consulting and Engineering SolutionsHamburgGermany
  4. 4.Department of MathematicsTechnical University of MunichMunichGermany

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