Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon |
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Authors: | A Rapaport P Cartigny |
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Institution: | (1) UMR Analyse des Systèmes et Biométrie, Montpellier, France;(2) GREQAM, Université de la Méditerranée, Marseille, France |
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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. |
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Keywords: | Calculus of variations Infinite horizon Viscosity solutions Hamilton-Jacobi equation Turnpikes |
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