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Properties of Hamiltonian systems in the Pontryagin maximum principle for economic growth problems

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Abstract

We consider an optimal control problem with a functional defined by an improper integral. We study the concavity properties of the maximized Hamiltonian and analyze the Hamiltonian systems in the Pontryagin maximum principle. On the basis of this analysis, we propose an algorithm for constructing an optimal trajectory by gluing the dynamics of the Hamiltonian systems. The algorithm is illustrated by calculating an optimal economic growth trajectory for macroeconomic data.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    A. A. Krasovskii & A. M. Tarasyev

Authors
  1. A. A. Krasovskii
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  2. A. M. Tarasyev
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Correspondence to A. A. Krasovskii.

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Original Russian Text © A.A. Krasovskii, A.M. Tarasyev, 2008, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 262, pp. 127–145.

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Krasovskii, A.A., Tarasyev, A.M. Properties of Hamiltonian systems in the Pontryagin maximum principle for economic growth problems. Proc. Steklov Inst. Math. 262, 121–138 (2008). https://doi.org/10.1134/S0081543808030103

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