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On the Infinite-Horizon Optimal Control of Age-Structured Systems

Author

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  • B. Skritek

    (Vienna University of Technology)

  • V. M. Veliov

    (Vienna University of Technology)

Abstract

The paper presents necessary optimality conditions of Pontryagin’s type for infinite-horizon optimal control problems for age-structured systems with state- and control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a “complete” set of optimality conditions is missing in the existing literature, because it is problematic to define in a sound way appropriate transversality conditions for the corresponding adjoint system. The main novelty is that (building on recent results by Aseev and the second author) the adjoint function in the Pontryagin principle is explicitly defined, which avoids the necessity of transversality conditions. The result is applied to several models considered in the literature.

Suggested Citation

  • B. Skritek & V. M. Veliov, 2015. "On the Infinite-Horizon Optimal Control of Age-Structured Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 243-271, October.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0680-x
    DOI: 10.1007/s10957-014-0680-x
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    References listed on IDEAS

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    1. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
    2. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    3. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
    4. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    5. Prskawetz, Alexia & Veliov, Vladimir M., 2007. "Age-specific dynamic labor demand and human capital investment," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3741-3777, December.
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    Cited by:

    1. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    2. Fabbri, Giorgio & Gozzi, Fausto & Zanco, Giovanni, 2021. "Verification results for age-structured models of economic–epidemics dynamics," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    3. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.
    4. B. Ainseba & L. Louison & A. Omrane, 2022. "A Population Harvesting Model with Time and Size Competition Dependence Function," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 647-665, November.

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