相关论文: Entropy-minimizing dynamical transport on Riemanni…
We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the…
We study a dynamic optimal transport type problem on a domain that consists of two parts: a compact set $\Omega \subset \mathbb{R}^d$ (bulk) and a non-intersecting and sufficiently regular curve $\Gamma \subset \Omega$. On each of them, a…
In this paper, we consider the Monge optimal transport problem with distance cost. We prove that in some metric spaces, possibly with many branching geodesics, an optimal transport map exists if the first marginal is absolutely continuous.…
We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects…
In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures. We formulate the above as a generalized optimal transport problem where the cost, the marginals, and the coupling…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The…
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schr\"odinger potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb{R}^ d$. Our results hold under mild assumptions on the marginal…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…
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.…
We prove the existence of an optimal map for the Monge problem when the cost is a supercritical Mane potential on a compact manifold. Supercritical Mane potentials form a class of costs which generalize the Riemannian distances. We describe…
Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of…
We prove that for two-marginal optimal transport with Coulomb cost, the optimal map is a $C^{1,\alpha}$ diffeomorphism outside a closed set of Lebesgue measure zero provided the marginals are $\alpha$-H\"older continuous and bounded away…
We study solutions to the multi-marginal Monge-Kantorovich problem which are concentrated on several graphs over the first marginal. We first present two general conditions on the cost function which ensure, respectively, that any solution…
We consider a multimarginal optimal transport, which includes as a particular case the Wasserstein barycenter problem. In this problem one has to find an optimal coupling between $m$ probability measures, which amounts to finding a tensor…
We study an entropic optimal transport problem in which the transport plan is penalized by a nonlinear convex functional acting on the coupling. We establish existence, uniqueness, and uniform a priori bounds for minimizers, and we show…
We propose a new metric between probability measures on a compact metric space that mirrors the Riemannian manifold-like structure of quadratic optimal transport but includes entropic regularization. Its metric tensor is given by the…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…