Stability of optimal traffic plans in the irrigation problem

Maria Colombo (1) , Antonio de Rosa (2, 3) , Andrea Marchese (4) , Paul Pegon (5, 6) , Antoine Prouff (7)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 Department of Mathematics [College Park]
3 BIDSA - Bocconi Institute for Data Science and Analytics
4 Department of mathematics/Dipartimento di Matematica [Univ. Trento]
5 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
6 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
7 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 result goes beyond the Eulerian stability proved in [Colombo, De Rosa, Marchese ; 2021], extending it to the Lagrangian framework.

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. Discrete and Continuous Dynamical Systems - Series A, In press, ⟨10.3934/dcds.2021167⟩. ⟨hal-02519237v2⟩