Related papers: Optimal Transportation with Capacity Constraints
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…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
The stability of solutions to optimal transport problems under variation of the measures is fundamental from a mathematical viewpoint: it is closely related to the convergence of numerical approaches to solve optimal transport problems and…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
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…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
We study optimal mass transport problems between two measures with respect to a non-traditional cost function, i.e. a cost $c$ which can attain the value $+\infty$. We define the notion of $c$-compatibility and strong-$c$-compatibility of…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
The optimal transportation problem, first suggested by Gaspard Monge in the 18th century and later revived in the 1940s by Leonid Kantorovich, deals with the question of transporting a certain measure to another, using transport maps or…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
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…
A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures $\mu$ on $\R^d$ which can be expressed as the moment measures of suitable convex functions $u$, i.e. are of the form $(\nabla u)\_\\#e^{- u}$ for…
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…
We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to…
In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We…
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…
Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study…
Consider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on the real line, and suppose the cost of matching two points satisfies the Monge condition. We introduce a notion of locally…