Related papers: Non-conservative optimal transport
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
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…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier. Our extension allows optimal transfer of unnormalized and unequal masses. We…
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane $\R^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the…
This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and…
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing…
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 a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…