Related papers: An explicit solution for a multimarginal mass tran…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under…
We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…
The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…
Generally, in transportation problem, full vehicles (e.g., light commercial vehicles, medium duty and heavy duty trucks, etc.) are to be booked, and transportation cost of a vehicle has to be paid irrespective of the fulfilment of the…
The transportation problem in the plane - how to move a set of objects from one set of points to another set of points in the cheapest way - is a very old problem going back several hundreds of years. In recent years the solution of the…
We solve the martingale optimal transport problem for cost functionals represented by optimal stopping problems. The measure-valued martingale approach developed in ArXiv: 1507.02651 allows us to obtain an equivalent infinite-dimensional…
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…
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 show the solvability of a multidimensional Muskat type initial boundary value problem. The proposed mathematical model describing the transport phenomena of non-homogeneous flow in porous media, relies on a generalized formulation of the…
A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
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…
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…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…
We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional law given the observation of the target, we characterize…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through…