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Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated 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…
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or $L^{p}$ regularization, general transport costs and…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
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…
We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of optimal transport potentials and maps, which are relevant…
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…
We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…
We study the solution of a large-scale transportation problem with an additional constraint on the sparsity of inbound flows. Such problems arise in the management of inventory for online retailers that operate with many order fulfillment…
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…
In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not…
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 study the most common image and informal description of the optimal transport problem for quadratic cost, also known as the second boundary value problem for the Monge--Amp\`{e}re equation -- What is the most efficient way to fill a hole…