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

Malte Braack (), Martin Quaas, Benjamin Tews () and Boris Vexler ()
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Malte Braack: University of Kiel
Benjamin Tews: P3 - Management Consulting and Engineering Solutions
Boris Vexler: Technical University of Munich

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 12, 950-972

Abstract: 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.

Keywords: Fishing strategies; Optimal control; Non-convex optimization; 35K20; 35K45; 35K57; 49K20; 49K40; 65M60 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1304-7

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