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Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon

Author

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  • A. Rapaport

    (UMR Analyse des Systèmes et Biométrie)

  • P. Cartigny

    (GREQAM, Université de la Méditerranée)

Abstract

Recently, the authors have proposed a new necessary and sufficient condition for turnpike optimality in calculus of variations with singular Euler equation. The method is based on a characterization of the value function and generalizes the well known method based on the Green theorem. Furthermore, it allows the optimality of a competition between several turnpikes to be characterized. For a class of such problems not enjoying the turnpike property, we give an explicit formula for the value function and show how to characterize the optimal solution as the limiting solution of a family of perturbed problems satisfying the turnpike property. The considered problems are scalar with infinite horizon.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:1:d:10.1007_s10957-007-9206-0
    DOI: 10.1007/s10957-007-9206-0
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    References listed on IDEAS

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    1. A. Rapaport & P. Cartigny, 2005. "Competition between Most Rapid Approach Paths: Necessary and Sufficient Conditions," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 1-27, January.
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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.
    2. 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.

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    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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