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On the Relation Between Turnpike Properties for Finite and Infinite Horizon Optimal Control Problems

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  • Lars Grüne

    (University of Bayreuth)

  • Christopher M. Kellett

    (University of Newcastle)

  • Steven R. Weller

    (University of Newcastle)

Abstract

We show that, under appropriate regularity conditions, a finite horizon optimal control problem exhibits the turnpike property, if and only if its infinite horizon counterpart does. We prove the result for both undiscounted and discounted problems and also provide a version which incorporates quantitative information about the convergence rates.

Suggested Citation

  • Lars Grüne & Christopher M. Kellett & Steven R. Weller, 2017. "On the Relation Between Turnpike Properties for Finite and Infinite Horizon Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 727-745, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-017-1103-6
    DOI: 10.1007/s10957-017-1103-6
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    References listed on IDEAS

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    1. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
    2. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    3. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    4. Alexander J. Zaslavski, 2014. "Turnpike Phenomenon and Infinite Horizon Optimal Control," Springer Optimization and Its Applications, Springer, edition 127, number 978-3-319-08828-0, September.
    5. J. v. Neumann, 1945. "A Model of General Economic Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 13(1), pages 1-9.
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    Cited by:

    1. Antoine Haddon & Héctor Ramírez & Alain Rapaport, 2019. "Optimal and Sub-optimal Feedback Controls for Biogas Production," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 642-670, November.

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