Related papers: Quantitative Uniqueness of Kantorovich Potentials
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschitz functions. This result has been widely used in various…
We investigate existence of dual optimizers in one-dimensional martingale optimal transport problems. While [BNT16] established such existence for weak (quasi-sure) duality, [BHP13] showed existence for the natural stronger pointwise…
We study a multi-marginal optimal transportation problem with a cost function of the form $c(x_{1}, \ldots,x_{m})=\sum_{k=1}^{m-1}|x_{k}-x_{k+1}|^{2} + |x_{m}- F(x_{1})|^{2}$, where $F: \mathbb{R}^n \rightarrow \mathbb{R}^n$. When $m=4$,…
We study a multi-marginal optimal transportation problem. Under certain conditions on the cost function and the first marginal, we prove that the solution to the relaxed, Kantorovich version of the problem induces a solution to the Monge…
This paper is concerned with an optimization problem governed by the Kantorovich optimal transportation problem. This gives rise to a bilevel optimization problem, which can be reformulated as a mathematical problem with complementarity…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
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 work we analyze regularized optimal transport problems in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, the aim is to find a transport plan, which is another Radon measure on the product of the…
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem can be reformulated as a mathematical problem with complementarity constraints in…
We investigate the problem of optimal transport in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, we seek an optimal transport plan which is another Radon measure on the product of the sets that has these…
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called potentials; equivalently, potentials can be defined as a…
In this paper, we want to establish some general results in the Lorentzian optimal transport theory that have well-known Riemannian counterparts. As a first result, we will provide non-trivial assumptions on the measures to ensure strong…
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…
Quadratically regularized optimal transport (QOT) is a sparse alternative to entropic optimal transport. We develop a quantitative stability theory for QOT under perturbations of the marginals, the transport cost function, and the…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
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.…
We develop a theory of optimal transport relative to a distinguished subset, which acts as a reservoir of mass, allowing us to compare measures of different total variation. This relative transportation problem has an optimal solution and…
We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an application, we determine optimal solutions of both the primal…