Related papers: A new transportation distance with bulk/interface …
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…
The problem of optimal mass transport arises in numerous applications including image registration, mesh generation, reflector design, and astrophysics. One approach to solving this problem is via the Monge-Amp\`ere equation. While recent…
Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is…
We identify a novel connection between a recently introduced pseudo-Riemannian framework for optimal mass transport and the geometry of Monge-Amp\`ere equations. We show this correspondence by application to an example from geophysical…
Here, we consider the planning problem for first-order mean-field games (MFG). When there is no coupling between players, MFG degenerate into optimal transport problems. Displacement convexity is a fundamental tool in optimal transport that…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
-In this paper, a novel resource allocation scheme based on discrete Cournot-Nash equilibria and optimal transport theory is proposed. The originality of this framework lies in the joint optimization of downlink bandwidth allocation and…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau…
We introduce and study a multi-marginal optimal partial transport problem. Under a natural and sharp condition on the dominating marginals, we establish uniqueness of the optimal plan. Our strategy of proof establishes and exploits a…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
We introduce a new class of distances between nonnegative Radon measures in Euclidean spaces. They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasserstein distances proposed by Benamou-Brenier and provide a…
Optimal transport has gained much attention in image processing field, such as computer vision, image interpolation and medical image registration. Recently, Bredies et al. (ESAIM:M2AN 54:2351-2382, 2020) and Schmitzer et al. (IEEE T MED…
Let $\Omega \subset \mathbb{R}^2$ be a bounded, convex domain and let $u$ be the solution of $-\Delta u = 1$ vanishing on the boundary $\partial \Omega$. The estimate $$ \| \nabla u\|_{L^{\infty}(\Omega)} \leq c |\Omega|^{1/2}$$ is…
We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…