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Maximum Principle for an Optimal Control Problem with an Asymptotic Endpoint Constraint

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Abstract

Under conditions characterizing the dominance of the discounting factor, a complete version of the Pontryagin maximum principle for an optimal control problem with infinite time horizon and a special asymptotic endpoint constraint is developed. Problems of this type arise in mathematical economics in the studies of growth models.

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Notes

  1. For details, see the work [6], where, in particular, necessary and sufficient conditions are obtained for the sustainability of optimal growth in an economy based on the exploitation of a renewable resource.

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Funding

This work was supported by the Russian Science Foundation (project no. 19-11-00223).

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Authors and Affiliations

  1. Steklov Mathematical Institute of the Russian Academy of Sciences, 119991, Moscow, Russia

    S. M. Aseev

  2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    S. M. Aseev

  3. International Institute for Applied Systems Analysis, A-2361, Laxenburg, Austria

    S. M. Aseev

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  1. S. M. Aseev
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Correspondence to S. M. Aseev.

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Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 27, No. 2, pp. 35 - 48, 2021 https://doi.org/10.21538/0134-4889-2021-27-2-35-48.

Translated by E. Vasil’eva

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Aseev, S.M. Maximum Principle for an Optimal Control Problem with an Asymptotic Endpoint Constraint. Proc. Steklov Inst. Math. 315 (Suppl 1), S42–S54 (2021). https://doi.org/10.1134/S0081543821060043

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