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Numerical methods for optimal control with binary control functions applied to a Lotka-Volterra type fishing problem. (English) Zbl 1107.49023

Seeger, Alberto (ed.), Recent advances in optimization. Proceedings of the twelfth French-German-Spanish conference on optimization, Avignon, France, September 20–24, 2004. Berlin: Springer (ISBN 3-540-28257-2/pbk). Lecture Notes in Economics and Mathematical Systems 563, 269-289 (2006).
A benchmark optimal control problem, where some or all of the control functions have the additional restriction to have values in set \(\{0,1\}\), are considered. The objective functional of the problem is of generalized Bólza type, containing Lagrange and Mayer terms. Several heuristics as well as a global approach based on a branch-and-bound strategy are described. The methods are successfully applied to an optimal control problem designed to control a fish population. Numerical results as well as solution methods are presented. The authors report on a good experience with the presented solution methods. Possibilities of further extensions of the methods to more general types of problems are briefly discussed in the concluding part of the paper.
For the entire collection see [Zbl 1079.90002].

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49M37 Numerical methods based on nonlinear programming

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