Related papers: The Monge optimal transport barycenter problem
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge-Amp\'ere equation and a transport equation. The system is the Eulerian formulation in the dual…
The theory of weak optimal transport (WOT), introduced by [Gozlan et al., 2017], generalizes the classic Monge-Kantorovich framework by allowing the transport cost between one point and the points it is matched with to be nonlinear. In the…
We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
We study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…
A natural and important question in multi-marginal optimal transport is whether the \emph{Monge ansatz} is justified; does there exist a solution of Monge, or deterministic, form? We address this question for the quadratic cost when each…
We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents…
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
We give a new probabilistic construction of solutions to real Monge-Amp\`ere equations in R^n satisfying the second boundary value problem with respect to a given target convex body P) which fits naturally into the theory of optimal…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
In the standard formulation of the denoising problem, one is given a probabilistic model relating a latent variable $\Theta \in \Omega \subset \mathbb{R}^m \; (m\ge 1)$ and an observation $Z \in \mathbb{R}^d$ according to: $Z \mid \Theta…
We shall present a measure theoretical approach for which together with the Kantorovich duality provide an efficient tool to study the optimal transport problem. Specifically, we study the support of optimal plans where the cost function…
We study an optimal process control problem with multiple assignable causes. The process is initially in-control but is subject to random transition to one of multiple out-of-control states due to assignable causes. The objective is to find…
The solution of conservation laws with parametrized shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop…
Given two probability densities on related data spaces, we seek a map pushing one density to the other while satisfying application-dependent constraints. For maps to have utility in a broad application space (including domain translation,…
We consider the problem of finding consistent upper price bounds and super replication strategies for exotic options, given the observation of call prices in the market. This field of research is called model-independent finance and has…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…