Related papers: Multi-marginal optimal transport: theory and appli…
We consider optimal transport problems where the cost is optimized over controlled dynamics and the end time is free. Unlike the classical setting, the search for optimal transport plans also requires the identification of optimal "stopping…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
These notes constitute a sort of Crash Course in Optimal Transport Theory. The different features of the problem of Monge-Kantorovitch are treated, starting from convex duality issues. The main properties of space of probability measures…
We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing…
Optimal transportation with capacity constraints, a variant of the well-known optimal transportation problem, is concerned with transporting one probability density $f \in L^1(\mathbb{R}^m)$ onto another one $g \in L^1(\mathbb{R}^n)$ so as…
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is…
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…
We discuss the Monge problem of mass transportation in the framework of stochastic thermodynamics and revisit the problem of the Landauer limit for finite-time thermodynamics, a problem that got the interest of Krzysztof Gawedzki in the…
We consider the theoretical properties of a model which encompasses bi-partite matching under transferable utility on the one hand, and hedonic pricing on the other. This framework is intimately connected to tripartite matching problems…
A natural and important question in multi-marginal optimal transport is whether the \emph{Monge ansatz} is justified; does there exist a solution of Monge, or deterministic, form? We address this question for the quadratic cost when each…
The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper/lower continuous capacities and to prove the cyclic monotonicity of the supports of optimal supermodular plans. As in the probabilistic…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…
We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X,dN) a possibly branching geodesic space. We show that under some assumptions on the…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and…
Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…