Stability of optimal traffic plans in the irrigation problem

Maria Colombo (1) , Antonio de Rosa (2) , Andrea Marchese (3) , Paul Pegon (4, 5) , Antoine Prouff (6)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 CIMS - Courant Institute of Mathematical Sciences [New York]
3 Department of mathematics/Dipartimento di Matematica [Univ. Trento]
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
5 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
6 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This is the Lagrangian counterpart of the recent Eulerian version proved in [CDM19a].

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Analyse classique [math.CA]

Maria Colombo, Antonio de Rosa, Andrea Marchese, Paul Pegon, Antoine Prouff. Stability of optimal traffic plans in the irrigation problem. 2020. ⟨hal-02519237v1⟩