Related papers: A multi-material transport problem and its convex …
In this paper we study general transportation problems in $\mathbb{R}^n$, in which $m$ different goods are moved simultaneously. The initial and final positions of the goods are prescribed by measures $\mu^-$, $\mu^+$ on $\mathbb{R}^n$ with…
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 this note we introduce a new model for the mailing problem in branched transportation in order to allow the cost functional to take into account the orientation of the moving particles. This gives an effective answer to [Problem 15.9] of…
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…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
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…
Generally, in transportation problem, full vehicles (e.g., light commercial vehicles, medium duty and heavy duty trucks, etc.) are to be booked, and transportation cost of a vehicle has to be paid irrespective of the fulfilment of the…
We consider the minimization of the $h$-mass over normal $1$-currents in $\mathbb{R}^n$ with coefficients in $\mathbb{R}^m$ and prescribed boundary. This optimization is known as multi-material transport problem and used in the context of…
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 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…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of 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…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
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…
Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results…
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