Related papers: A fast approach to optimal transport: The back-and…
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…
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.…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…
We prove existence of an optimal transport map in the Monge-Kantorovich problem associated to a cost $c(x,y)$ which is not finite everywhere, but coincides with $|x-y|^2$ if the displacement $y-x$ belongs to a given convex set $C$ and it is…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…
We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color images…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
We study the Lagrangian formulation of a class of the Monge-Kantorovich optimal transportation problem. It can be considered a stochastic optimal transportation problem for absolutely continuous stochastic processes. A cost function and…
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…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
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…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
Smart city has been consider the wave of the future and the route recommendation in networks is a fundamental problem in it. Most existing approaches for the shortest route problem consider that there is only one kind of cost in networks.…
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…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
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…