Competition between Most Rapid Approach Paths: Necessary and Sufficient Conditions

A. Rapaport and P. Cartigny
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A. Rapaport: UMR Analyse des Systèmes et Biométrie
P. Cartigny: GREQAM, Université de la Méditerranée

Journal of Optimization Theory and Applications, 2005, vol. 124, issue 1, No 1, 27 pages

Abstract: 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.

Keywords: Calculus of variations; infinite horizon; viscosity solutions; Hamilton-Jacobi equation; turnpikes (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-004-6463-z

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