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Necessary Conditions for the Optimality and Sustainability of Solutions in Infinite-Horizon Optimal Control Problems

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  • Sergey M. Aseev

    (Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina St., 119991 Moscow, Russia
    Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991 Moscow, Russia)

Abstract

The paper deals with an infinite-horizon optimal control problem with general asymptotic endpoint constraints. The fulfillment of constraints of this type can be viewed as the minimal necessary condition for the sustainability of solutions. A new version of the Pontryagin maximum principle with an explicitly specified adjoint variable is developed. The proof of the main results is based on the fact that the restriction of the optimal process to any finite time interval is a solution to the corresponding finite-horizon problem containing the conditional cost of the phase vector as a terminal term.

Suggested Citation

  • Sergey M. Aseev, 2023. "Necessary Conditions for the Optimality and Sustainability of Solutions in Infinite-Horizon Optimal Control Problems," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3851-:d:1236102
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    References listed on IDEAS

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    1. Simone Valente, 2005. "Sustainable Development, Renewable Resources and Technological Progress," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 30(1), pages 115-125, January.
    2. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Simone Valente, 2008. "Optimal Growth, Genuine Savings And Long‐Run Dynamics," Scottish Journal of Political Economy, Scottish Economic Society, vol. 55(2), pages 210-226, May.
    4. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
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