Scandinavian Working Papers in Economics

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

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

Leif K. Sandal () and Gerhard Berge ()
Additional contact information
Leif K. Sandal: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Gerhard Berge: Dept. of Mathematics, University of Bergen, Postal: Department of Mathematics, University of Bergen , J. Bruns gt 12, N-5008 Bergen, Norway

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

JEL-codes: C61; C63; Q00

21 pages, March 12, 2004

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