相关论文: $L^\infty$-optimal transport for a class of quasic…
In this note, we propose polynomial-time algorithms solving the Monge and Kantorovich formulations of the $\infty$-optimal transport problem in the discrete and finite setting. It is the first time, to the best of our knowledge, that…
We establish that solving an optimal transportation problem in which the source and target densities are defined on manifolds with different dimensions, is equivalent to solving a new nonlocal analog of the Monge-Amp\`ere equation,…
We consider Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge…
The optimal weak transport problem has recently been introduced by Gozlan et.\ al. We provide general existence and duality results for these problems on arbitrary Polish spaces, as well as a necessary and sufficient optimality criterion in…
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
The $L^1$ optimal transport density $\mu^*$ is the unique $L^\infty$ solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of the $L^1$ -transport energy functional E. In the present…
Let $M,N$ be two smooth compact hypersurfaces of $\mathbb{R}^n$ which bound strictly convex domains equipped with two absolutely continuous measures $\mu$ and $\nu$ (with respect to the volume measures of $M$ and $N$). We consider the…
We prove a new sample complexity result for divergence regularized optimal transport. Our bound holds for probability measures on~$\mathbb{R}^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz…
In this paper, we study the regularity of optimal mappings in Monge's mass transfer problem. Using the approximation to Monge's cost function given by the Euclidean distance c(x,y)=dist(x,y) through the costs…
Constraining the maximum likelihood density estimator to satisfy a sufficiently strong constraint, $\log-$concavity being a common example, has the effect of restoring consistency without requiring additional parameters. Since many results…
In this short note, we show that given a cost function $c$, any coupling $\pi$ of two probability measures where the second is a discrete measure can be associated to a certain bipartite graph containing a perfect matching, based on the…
Two recent works, Avella-Medina and Gonz\'alez-Sanz (2026) and Passeggeri and Paindaveine (2026), studied the robustness of the optimal transport map through its breakdown point, i.e., the smallest fraction of contamination that can make…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry…
We study an entropic optimal transport problem in which the transport plan is penalized by a nonlinear convex functional acting on the coupling. We establish existence, uniqueness, and uniform a priori bounds for minimizers, and we show…
Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the…
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal…
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails…