A Benamou-Brenier approach to branched transport

Lorenzo Brasco (1, 2) , Giuseppe Buttazzo (2) , Filippo Santambrogio (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di Matematica [Pisa]

The problem of branched transportation aims to describe the movement of masses when, due to concavity effects, they have the interest to travel together as much as possible, because the cost for a path of length l covered by a mass m is proportional to a concave power m^a l. The optimization of this criterion let branched structures appear and is suitable to applications like road systems, blood vessels, river networks\dots Several models have been employed in the literature to present this transport problem, and the present paper looks at a dynamical one, similar to the celebrated Benamou-Brenier formulation of Kantorovitch optimal transport. The movement is represented by a path of probabilities, satisfying the continuity equation together with a velocity field v. The transportation cost to be minimized is non-convex and finite only on atomic measures.

Domaines: Optimisation et contrôle [math.OC]

Lorenzo Brasco, Giuseppe Buttazzo, Filippo Santambrogio. A Benamou-Brenier approach to branched transport. 2010. ⟨hal-00474371⟩