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A method for numerical and analytical solutions to a class of nonlinear optimal control problems

Author

Listed:
  • Sandal, Leif K.

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Berge, Gerhard

    (Dept. of Mathematics, University of Bergen)

Abstract

Dynamic optimization problems cover a great class of problems in theoretical and applied economics and technology. In this account the exploitation of a general renewable capital stock is modeled through an alternative formulation to the classical optimal control approach. We propose a very simple alternating iterative algorithm that is shown to converge very fast towards a solution, where the accuracy of the solution can also be determined. The algorithm can also produce approximate closed form (analytical) feedback solutions. By using a special simple seed in the iteration scheme we reproduce perturbation results (formulae) that are published in the last decade. Often only two or three iteration steps are necessary to produce sufficiently accurate approximations.

Suggested Citation

  • Sandal, Leif K. & Berge, Gerhard, 2004. "A method for numerical and analytical solutions to a class of nonlinear optimal control problems," Discussion Papers 2004/2, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2004_002
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    File URL: http://hdl.handle.net/11250/164068
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    References listed on IDEAS

    as
    1. R. Quentin Grafton & Leif K. Sandal & Stein Ivar Steinshamn, 2000. "How to Improve the Management of Renewable Resources: The Case of Canada's Northern Cod Fishery," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 82(3), pages 570-580.
    2. LK Sandal & SI Steinshamn, 2001. "A Bio‐Economic Model For Namibian Pilchard," South African Journal of Economics, Economic Society of South Africa, vol. 69(2), pages 299-318, June.
    3. Ragnar Arnason & Leif K. Sandal & Stein Ivar Steinshamn & Niels Vestergaard, 2004. "Optimal Feedback Controls: Comparative Evaluation of the Cod Fisheries in Denmark, Iceland, and Norway," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 531-542.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Capital Dynamics Modeling; Natural Resource Exploitation; Analytical and Numerical Contraction;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • Q00 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - General

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