Related papers: A multi-material transport problem with arbitrary …
Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this…
In this paper, we study the pickup and delivery problem with multiple transportation modalities, and address the challenge of efficiently allocating transportation resources while price matching users with their desired delivery modes. More…
Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called…
We study a multi-marginal optimal transportation problem on a Riemannian manifold, with cost function given by the average distance squared from multiple points to their barycenter. Under a standard regularity condition on the first…
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y -- x|. The selected plan at the limit is, among those which are optimal for the non-penalized problem,…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
We study the structure of martingale transports in finite dimensions. We consider the family $\mathcal{M}(\mu,\nu) $ of martingale measures on $\mathbb{R}^N \times \mathbb{R}^N$ with given marginals $\mu,\nu$, and construct a family of…
Despite the ubiquity of transportation data, methods to infer the state parameters of a network either ignore sensitivity of route decisions, require route enumeration for parameterizing descriptive models of route selection, or require…
We consider optimal transport problems where the cost for transporting a given probability measure $\mu_0$ to another one $\mu_1$ consists of two parts: the first one measures the transportation from $\mu_0$ to an intermediate (pivot)…
We provide an explicit algorithm to solve the idempotent analogue of the discrete Monge-Kantorovich optimal mass transportation problem with the usual real number field replaced by the tropical (max-plus) semiring, in which addition is…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
We investigate a new multi-marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we introduce such dissociation model, the corresponding…
For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
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…
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…
Numerically solving multi-marginal optimal transport (MMOT) problems is computationally prohibitive, even for moderate-scale instances involving $l\ge4$ marginals with support sizes of $N\ge1000$. The cost in MMOT is represented as a tensor…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…