Nonturnpike optimal solutions and their approximations in infinite horizon
Résumé
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 but that do not enjoy the turnpike property, we give an explicit formula for the value function and show how to characterize the optimal solution as a limiting solution of a family of perturbed problems, satisfying the turnpike property. The considered problems are scalar with infinite horizon.