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

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2004/2.

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Length: 21 pages
Date of creation: 12 Mar 2004
Date of revision:
Handle: RePEc:hhs:nhhfms:2004_002

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Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Phone: +47 55 95 92 93
Fax: +47 55 95 96 50
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Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Related research

Keywords: Capital Dynamics Modeling; Natural Resource Exploitation; Analytical and Numerical Contraction;

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  1. 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.
  2. 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.
  3. 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, 06.
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