IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v145y2010i3d10.1007_s10957-010-9677-2.html
   My bibliography  Save this article

Stability of a Turnpike Phenomenon for a Discrete-Time Optimal Control System

Author

Listed:
  • A. J. Zaslavski

    (Technion)

Abstract

We study the structure of solutions of a discrete-time control system with a compact metric space of states X which arises in economic dynamics. This control system is described by a nonempty closed set Ω⊂X×X which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous objective function v:Ω→R 1 which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. In the present paper, we show that these turnpike properties are stable under perturbations of the objective function v.

Suggested Citation

  • A. J. Zaslavski, 2010. "Stability of a Turnpike Phenomenon for a Discrete-Time Optimal Control System," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 597-612, June.
  • Handle: RePEc:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-010-9677-2
    DOI: 10.1007/s10957-010-9677-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9677-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-010-9677-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. Rapaport & P. Cartigny, 2007. "Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 1-14, July.
    2. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    3. M. Khan & Tapan Mitra, 2006. "Undiscounted optimal growth in the two-sector Robinson-Solow-Srinivasan model: a synthesis of the value-loss approach and dynamic programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 341-362, October.
    4. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.
    5. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2005. "Bias and overtaking equilibria for zero-sum continuous-time Markov games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 437-454, July.
    6. Sabine Pickenhain & Valeriya Lykina, 2006. "Sufficiency Conditions for Infinite Horizon Optimal Control Problems," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 217-232, Springer.
    7. J. Blot & P. Cartigny, 2000. "Optimality in Infinite-Horizon Variational Problems under Sign Conditions," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 411-419, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Minako Fujio, 2009. "Optimal Transition Dynamics In The Leontief Two‐Sector Growth Model With Durable Capital: The Case Of Capital Intensive Consumption Goods," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 490-511, December.
    2. M. Ali Khan & Adriana Piazza, 2010. "On uniform convergence of undiscounted optimal programs in the Mitra–Wan forestry model: The strictly concave case," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 57-76, March.
    3. Ali Khan, M. & Piazza, Adriana, 2012. "On the Mitra–Wan forestry model: A unified analysis," Journal of Economic Theory, Elsevier, vol. 147(1), pages 230-260.
    4. Ali Khan, M. & Mitra, Tapan, 2008. "Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 707-732, July.
    5. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.
    6. Metcalf, Christopher J., 2008. "The dynamics of the Stiglitz policy in the RSS model," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 652-661.
    7. Alexander J. Zaslavski, 2023. "An Optimal Control Problem Related to the RSS Model," Mathematics, MDPI, vol. 11(17), pages 1-14, September.
    8. M. Khan & Alexander Zaslavski, 2010. "On locally optimal programs in the Robinson–Solow–Srinivasan model," Journal of Economics, Springer, vol. 99(1), pages 65-92, February.
    9. Khalifa, Sherif, 2011. "Undiscounted optimal growth with consumable capital and labor-intensive consumption goods," Economic Modelling, Elsevier, vol. 28(4), pages 1673-1682, July.
    10. Khan, M. Ali & Zaslavski, Alexander J., 2009. "On existence of optimal programs: The RSS model without concavity assumptions on felicities," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 624-633, September.
    11. M. Khan & Alexander Zaslavski, 2007. "On a Uniform Turnpike of the Third Kind in the Robinson-Solow-Srinivasan Model," Journal of Economics, Springer, vol. 92(2), pages 137-166, October.
    12. Liuchun Deng & Minako Fujio & M. Ali Khan, 2021. "Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 615-639, September.
    13. Fujio, Minako & Lei, Yan & Deng, Liuchun & Khan, M. Ali, 2021. "The miniature two-sector model of optimal growth: The neglected case of a capital-intensive investment-good sector," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 662-671.
    14. Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.
    15. Rodolphe Dos Santos Ferreira & Frédéric Dufourt, 2013. "On Stabilization Policy in Sunspot-Driven Oligopolistic Economies," AMSE Working Papers 1337, Aix-Marseille School of Economics, France, revised 30 Jun 2013.
    16. Robert M. Solow, 2000. "La teoria neoclassica della crescita e della distribuzione," Moneta e Credito, Economia civile, vol. 53(210), pages 149-185.
    17. Zilcha, Itzhak, 1981. "Competitive Prices and Optimality in Multisector Economy with Changing Preferences," Foerder Institute for Economic Research Working Papers 275343, Tel-Aviv University > Foerder Institute for Economic Research.
    18. Tapan Mitra & Kazuo Nishimura, 2012. "Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 195-233, Springer.
    19. Ali Khan, M. & Schlee, Edward E., 2017. "The nonconcavity of money-metric utility: A new formulation and proof," Economics Letters, Elsevier, vol. 154(C), pages 10-12.
    20. Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," Post-Print halshs-00096034, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-010-9677-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.