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Competition between Most Rapid Approach Paths: Necessary and Sufficient Conditions

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  • A. Rapaport

    (UMR Analyse des Systèmes et Biométrie)

  • P. Cartigny

    (GREQAM, Université de la Méditerranée)

Abstract

We revisit the optimality of the most rapid approach paths for problems of the calculus of variation in infinite horizon, which are scalar and linear w.r.t. the derivative. Our approach is based on the characterization of the value function in terms of the viscosity solutions of a Hamilton-Jacobi equation. We obtain a new necessary and sufficient condition when there is only one turnpike, but characterize also the optimality of several turnpikes in competition. In this last case, nonsmooth analysis is used. Finally, we illustrate the results on a fishery management problem, for which the growth function has a depensation and the price is variable.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6463-z
    DOI: 10.1007/s10957-004-6463-z
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    References listed on IDEAS

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    1. Spence, A Michael & Starrett, David, 1975. "Most Rapid Approach Paths in Accumulation Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 388-403, June.
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    Cited by:

    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. 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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