相关论文: A Benamou-Brenier approach to branched transport
We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
In branched transportation problems mass has to be transported from a given initial distribution to a given final distribution, where the cost of the transport is proportional to the transport distance, but subadditive in the transported…
In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities are transported simultaneously along a network. The cost of…
We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book…
This article generalizes the study of branched/ramified optimal transportation to those with capacity constraints. Each admissible transport network studied here is represented by a transport multi-path between measures, with a capacity…
We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but…
We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…
We consider two variational models for transport networks, an urban planning and a branched transport model, in both of which there is a preference for networks that collect and transport lots of mass together rather than transporting all…
We introduce and study a new optimal transport problem on a bounded domain $\bar\Omega \subset \mathbb R^d$, defined via a dynamical Benamou-Brenier formulation. The model handles differently the motion in the interior and on the boundary,…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under…
We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
The Gilbert--Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transport plan. A specific feature of the problem is that the cost…
In this paper we analyze a mass transportation problem in a bounded domain with the possibility to transport mass to/from the boundary, paying the transport cost, that is given by the Euclidean distance plus an extra cost depending on the…
It is well-known that the optimal transport problem on the real line for the classical distance cost may not have a unique solution. In this paper we recover uniqueness by considering the transport problems where the costs are a power…
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible…
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…