Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexample

Bruno Ziliotto (1, 2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CNRS - Centre National de la Recherche Scientifique
3 Université Paris Dauphine-PSL

This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive Hamiltonian.

Domaines: Optimisation et contrôle [math.OC]

Bruno Ziliotto. Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexample. Journal de Mathématiques Pures et Appliquées, 2019, 128, pp.330-338. ⟨10.1016/j.matpur.2019.04.005⟩. ⟨hal-01936579⟩