Optimal transport with convex obstacle

Pierre Cardaliaguet (1) , Chloé Jimenez (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LM - Laboratoire de mathématiques de Brest

We consider the Monge transportation problem when the cost is the squared geodesic distance around a convex obstacle. We show that there exists at least one---and in general infinitely many---optimal transport maps.

Mots clés: Geodesic; Transportation problem

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Chloé Jimenez. Optimal transport with convex obstacle. Journal of Mathematical Analysis and Applications, 2011, 381 (1), pp.43-63. ⟨10.1016/j.jmaa.2011.04.007⟩. ⟨hal-00657559⟩