Related papers: Computing the time-continuous Optimal Mass Transpo…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
We introduce a stochastic optimal transport for the Langevin dynamics with positive mass and study its zero--mass limit. The new aspect of this paper is that we only fix the initial and terminal probability distributions of the positions of…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
Grogan et al [11,12] have recently proposed a solution to colour transfer by minimising the Euclidean distance L2 between two probability density functions capturing the colour distributions of two images (palette and target). It was shown…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Planning trajectories for automated vehicles in urban environments requires methods with high generality, long planning horizons, and fast update rates. Using a path-velocity decomposition, we contribute a novel planning framework, which…
In this paper, we first present a centralized traffic control model based on the emerging dynamic path flows. This new model in essence views the whole target network as one integral piece in which traffic propagates based on traffic flow…
Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we…
The Lambert problem originated in orbital mechanics. It concerns with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravitational potential with additional time horizon and endpoint…
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…
Given $n$ points in a circular region $C$ in the plane, we study the problems of moving the $n$ points to its boundary to form a regular $n$-gon such that the maximum (min-max) or the sum (min-sum) of the Euclidean distances traveled by the…
Given a $d$-dimensional continuous (resp. discrete) probability distribution $\mu$ and a discrete distribution $\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass…
We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
Regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model…
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…
In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…