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Department of Business and Management Science, Norwegian School of Economics (NHH) Discussion Papers, Department of Business and Management Science, Norwegian School of Economics (NHH)

No 2004/2:
A method for numerical and analytical solutions to a class of nonlinear optimal control problems

Leif K. Sandal () and Gerhard Berge ()

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.

Keywords: Capital Dynamics Modeling; Natural Resource Exploitation; Analytical and Numerical Contraction; (follow links to similar papers)

JEL-Codes: C61; C63; Q00; (follow links to similar papers)

21 pages, March 12, 2004

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