The geometry of optimal transportation
From MaRDI portal
Publication:1373007
DOI10.1007/BF02392620zbMath0887.49017OpenAlexW2096413780WikidataQ63508067 ScholiaQ63508067MaRDI QIDQ1373007
Wilfrid Gangbo, Robert J. McCann
Publication date: 5 November 1997
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392620
cost functionsmeasure-preserving transformationMonge's problemKantorovich's problemminimum-cost transformations
Transportation, logistics and supply chain management (90B06) Trade models (91B60) Existence theories in calculus of variations and optimal control (49J99)
Related Items
Regularity of optimal transport on compact, locally nearly spherical, manifolds, Embedding \(\mathbb S^n\) into \(\mathbb R^{n+1}\) with given integral Gauss curvature and optimal mass transport on \(\mathbb S^n\), The directional optimal transport, Local semiconvexity of Kantorovich potentials on non-compact manifolds, Minimax confidence intervals for the sliced Wasserstein distance, Second order variational heuristics for the Monge problem on compact manifolds, Primal dual methods for Wasserstein gradient flows, Entropic and Displacement Interpolation: A Computational Approach Using the Hilbert Metric, Optimal Transport and Curvature, The non-relativistic limit of the Vlasov-Maxwell system with uniform macroscopic bounds, Regularity of potential functions of the optimal transportation problem, The semigeostrophic equations discretized in reference and dual variables, When optimal transport meets information geometry, Pseudo-Riemannian geometry encodes information geometry in optimal transport, Optimally solving a transportation problem using Voronoi diagrams, Limit laws for empirical optimal solutions in random linear programs, A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures, On the Degeneracy of Optimal Transportation, Optimal transport maps on Alexandrov spaces revisited, Exponential convergence of parabolic optimal transport on bounded domains, Darcy's law with a source term, The Monge–Ampère equation and its link to optimal transportation, The geometry of multi-marginal Skorokhod embedding, Transport maps, non-branching sets of geodesics and measure rigidity, Weak monotone rearrangement on the line, On the structure of optimal transportation plans between discrete measures, Optimal controlled transports with free end times subject to import/export tariffs, The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains, Optimal measure transportation with respect to non-traditional costs, The optimal mass transport problem for relativistic costs, The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation, The Kähler geometry of certain optimal transport problems, Structural results on convexity relative to cost functions, On the uniqueness of minimizers for a class of variational problems with polyconvex integrand, Asymptotic analysis of domain decomposition for optimal transport, Mass transportation and the consistency of the empirical optimal conditional locations, Multiplicative Schrödinger problem and the Dirichlet transport, A note on the differentiability of the Hellinger-Kantorovich distances, Solutions to multi-marginal optimal transport problems concentrated on several graphs, Optimal transportation between unequal dimensions, A fast approach to optimal transport: the back-and-forth method, Martingale Benamou-Brenier: a probabilistic perspective, Uniquely minimizing costs for the Kantorovitch problem, Characterization of toric systems via transport costs, Multi-marginal maximal monotonicity and convex analysis, Unnormalized optimal transport, A perturbation argument for a Monge-Ampère type equation arising in optimal transportation, Boundary regularity of optimal transport paths, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, Optimal transport: discretization and algorithms, Optimal martingale transport between radially symmetric marginals in general dimensions, Rotation numbers for measure-valued circle maps, On the sufficiency of \(c\)-cyclical monotonicity for optimality of transport plans, Extended least action principle for steady flows under a prescribed flux, On a Kantorovich problem with a density constraint, Equilibrium structure of a bidimensional asymmetric city, THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION, Duality for Borel measurable cost functions, Symmetry of solutions to parabolic Monge-Ampère equations, Discretisation and duality of optimal Skorokhod embedding problems, Boundary \(\varepsilon\)-regularity in optimal transportation, Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs, On the existence and weak stability of solutions to the compressible semigeostrophic equations, On asymptotic behaviour and \(W^{2, p}\) regularity of potentials in optimal transportation, Continuity and injectivity of optimal maps, Minimal measures, one-dimensional currents and the Monge-Kantorovich problem, A unified approach to coupling SDEs driven by Lévy noise and some applications, Stability of flows associated to gradient vector fields and convergence of iterated transport maps, Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds, Optimal Transport and Cournot-Nash Equilibria, Lp theory for the multidimensional aggregation equation, Data-Driven Optimal Transport, A solution to the Monge transport problem for Brownian martingales, Stochastic optimal transport with free end time, Existence and uniqueness of optimal transport maps obtained by the secondary variational method, Ramified optimal transportation in geodesic metric spaces, Kantorovich problems and conditional measures depending on a parameter, Domain decomposition for entropy regularized optimal transport, On displacement interpolation of measures involved in Brenier’s theorem, Quasiconvexity and relaxation in optimal transportation of closed differential forms, A Rockafellar-type theorem for non-traditional costs, Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula, Kantorovich problems with a parameter and density constraints, Applications of weak transport theory, Constructing time-homogeneous generalized diffusions consistent with optimal stopping values, Interpolating between matching and hedonic pricing models, Existence in multidimensional screening with general nonlinear preferences, Convergence of a Newton algorithm for semi-discrete optimal transport, The Kantorovich metric: the initial history and little-known applications, Optimality conditions and exact solutions of the two-dimensional Monge-Kantorovich problem, Existence, duality, and cyclical monotonicity for weak transport costs, Cortically based optimal transport, Optimal stability estimates and a new uniqueness result for advection-diffusion equations, Synchronic and Asynchronic Descriptions of Irrigation Problems, Entropic optimal transport: geometry and large deviations, General construction and classes of explicit \(L^1\)-optimal couplings, Optimal transportation, topology and uniqueness, Optimal transport and integer partitions, Recent developments on the MTW tensor, Optimal transport and Skorokhod embedding, A Continuation Multiple Shooting Method for Wasserstein Geodesic Equation, Optimal transportation, modelling and numerical simulation, THE MULTI-MARGINAL OPTIMAL PARTIAL TRANSPORT PROBLEM, Large data limit for a phase transition model with the p-Laplacian on point clouds, On the matrix Monge–Kantorovich problem, Pair Densities in Density Functional Theory, Vector and Matrix Optimal Mass Transport: Theory, Algorithm, and Applications, A new $L^\infty$ estimate in optimal mass transport, Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms, Lagrangian Discretization of Variational Mean Field Games, The Entropic Regularization of the Monge Problem on the Real Line, Convergence Rates for Upwind Schemes with Rough Coefficients, Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with $L^1$ Vorticity, A non‐linear monotonicity principle and applications to Schrödinger‐type problems, Template-based CT reconstruction with optimal transport and total generalized variation, Optimal Transport via a Monge--Ampère Optimization Problem, Minimizing optimal transport for functions with fixed-size nodal sets, Maximal Monotonicity and Cyclic Involutivity of Multiconjugate Convex Functions, An optimal-transport finite-particle method for mass diffusion, Convex geometry of finite exchangeable laws and de Finetti style representation with universal correlated corrections, Dynamical optimal transport of nonlinear control-affine systems, An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems, Monge solutions and uniqueness in multi-marginal optimal transport via graph theory, Geodesics of minimal length in the set of probability measures on graphs, A new proof of uniqueness of solutions to kinetic Cucker-Smale model based on optimal transport methods, Geometry of vectorial martingale optimal transportations and duality, On the difference between entropic cost and the optimal transport cost, Sharp convergence rates for empirical optimal transport with smooth costs, The global classical solution and asymptotic behavior of the Cauchy problem for hyperbolic Monge-Ampère equation, A Continuation Method in Bayesian Inference, Generalized curvature for the optimal transport problem induced by a Tonelli Lagrangian, The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities, Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology, Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning, Optimal Transport Approximation of 2-Dimensional Measures, Central limit theorems for semi-discrete Wasserstein distances, Fine properties of geodesics and geodesic \(\lambda\)-convexity for the Hellinger-Kantorovich distance, Mumford–Shah functionals on graphs and their asymptotics, Optimal transport approach to Michael-Simon-Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds, Measuring linear correlation between random vectors, Limit theorems for entropic optimal transport maps and Sinkhorn divergence, Displacement Interpolation Using Monotone Rearrangement, Optimal Transport with Controlled Dynamics and Free End Times, On a Solution to the Monge Transport Problem on the Real Line Arising from the Strictly Concave Case, Optimal transportation for the determinant, Optimal Brownian Stopping When the Source and Target Are Radially Symmetric Distributions, Gradient projection methods for the $n$-coupling problem, Asymptotic analysis of the Ginzburg–Landau functional on point clouds, Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations, On one-dimensionality of metric measure spaces, Concentration on the Discrete Torus Using Transportation, Multilevel Optimal Transport: A Fast Approximation of Wasserstein-1 Distances, MASS TRANSPORTATION IN GROUPS OF TYPE H, Chain Rule Optimal Transport, Density Functional Theory and Optimal Transportation with Coulomb Cost, Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space, Information geometry and non-equilibrium thermodynamic relations in the over-damped stochastic processes, Lower Bounds for the Counting Function of an Integral Operator, Parameter Dependent Optimal Thresholds, Indifference Levels and Inverse Optimal Stopping Problems, A JKO Splitting Scheme for Kantorovich--Fisher--Rao Gradient Flows, Strong convexity of sandwiched entropies and related optimization problems, Optimal Multiphase Transportation with prescribed momentum, An Algorithm for Optimal Transport between a Simplex Soup and a Point Cloud, Optimal transportation on non-compact manifolds, On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations, An optimal matching problem, Caractérisation d'une solution optimale au problème de Monge-Kantorovitch, Numerical resolution of an “unbalanced” mass transport problem, Sharp summability for Monge Transport densityviaInterpolation, OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS, MODELLING VASCULAR MORPHOGENESIS: CURRENT VIEWS ON BLOOD VESSELS DEVELOPMENT, Adaptivity with moving grids, Mathematical methods in medical image processing, Optimal Transport for the System of Isentropic Euler Equations, Kurdyka–Łojasiewicz–Simon inequality for gradient flows in metric spaces, Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge, Optimal transportation with capacity constraints, Dynamic and stochastic propagation of the Brenier optimal mass transport, A minimizing Movement approach to a class of scalar reaction–diffusion equations, The back-and-forth method for Wasserstein gradient flows, Existence of optimal maps in the reflector-type problems, Multi-Marginal Optimal Transportation Problem for Cyclic Costs, A tumor growth model of Hele-Shaw type as a gradient flow, The Hartree and Vlasov equations at positive density, Lubrication approximation with prescribed nonzero contact anggle, Cyclical monotonicity and the ergodic theorem, Geometry of the Schrödinger equation and stochastic mass transportation, Boundary $C^{1,\alpha}$ regularity of an optimal transport problem with cost close to $-x\cdot y$, The $L^1$-contraction principle in optimal transport, Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations, An order inequality characterizing invariant barycenters on symmetric cones, On the relation between optimal transport and Schrödinger bridges: a stochastic control viewpoint, Geometry of distribution-constrained optimal stopping problems, On strict convexity and continuous differentiability of potential functions in optimal transportation, Euler-Poisson systems as action-minimizing paths in the Wasserstein space, Ricci curvature, isoperimetry and a non-additive entropy, Symmetry analysis of an equation for constrained optimal transport, modelling the distribution of ants round a nest, An efficient algorithm for matrix-valued and vector-valued optimal mass transport, Prescription of Gauss curvature using optimal mass transport, Optimal partition of a large labor force into working pairs, Hedonic price equilibria, stable matching, and optimal transport: Equivalence, topology, and uniqueness, The Monge problem for supercritical Mañé potentials on compact manifolds, A sparse multiscale algorithm for dense optimal transport, A family of functional inequalities: Łojasiewicz inequalities and displacement convex functions, Dynamics of optimal partial transport, Duality theorem for the stochastic optimal control problem, Variational approximation for Fokker-Planck equation on Riemannian manifold, Numerical solution of the optimal transportation problem using the Monge-Ampère equation, Minimization for conditional simulation: relationship to optimal transport, Uniqueness of the solution to the Vlasov--Poisson system with bounded density, On Monge-Ampère type equations arising in optimal transportation problems, The Monge problem in Banach spaces, Optimal transport from Lebesgue to Poisson, A continuous linear optimal transport approach for pattern analysis in image datasets, Monotonicity of time-dependent transportation costs and coupling by reflection, Maximal coupling of Euclidean Brownian motions, The Monge problem for strictly convex norms in \(\mathbb R^d\), Surface parameterization based on polar factorization, Prescription of Gauss curvature on compact hyperbolic orbifolds, On the twist condition and \(c\)-monotone transport plans, Optimal transport and large number of particles, A glimpse into the differential topology and geometry of optimal transport, Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutions, Integrability of optimal mappings, The exchange value embedded in a transport system, Reprint of: Optimally solving a transportation problem using Voronoi diagrams, Regularity of densities in relaxed and penalized average distance problem, Hölder continuity and injectivity of optimal maps, Transportation distances on the circle, On the regularity of solutions of optimal transportation problems, Kantorovich potentials and continuity of total cost for relativistic cost functions, Metric currents and geometry of Wasserstein spaces, A planning problem combining calculus of variations and optimal transport, Symplectic factorization, Darboux theorem and ellipticity, A variational approach to some transport inequalities, Remarks on the stability of mass minimizing currents in the Monge-Kantorovich problem, Remarks on the Monge-Kantorovich problem in the discrete setting, Refined second law of thermodynamics for fast random processes, Homogenization for a class of integral functionals in spaces of probability measures, Optimal transportation for a quadratic cost with convex constraints and applications, From the heat measure to the pinned Wiener measure on loop groups, Measure concentration and the weak Pinsker property, On duality for a generalized Monge--Kantorovich problem., Optimal mass transportation in the Heisenberg group., Foreword to the special issue devoted to Professor Ivar Ekeland's 70th birthday, Steering the distribution of agents in mean-field games system, Structure of optimal martingale transport plans in general dimensions, On the local structure of optimal measures in the multi-marginal optimal transportation problem, Wasserstein geometry of Gaussian measures, On the free boundary associated with the stationary Monge-Ampère operator on the set of non strictly convex functions, On the local geometry of maps with c-convex potentials, Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations, Infinite-body optimal transport with Coulomb cost, A study of the dual problem of the one-dimensional \(L^\infty\)-optimal transport problem with applications, Academic wages and pyramid schemes: a mathematical model, The intrinsic dynamics of optimal transport, Wasserstein barycenters over Riemannian manifolds, Existence and uniqueness of optimal maps on Alexandrov spaces, Embedding optimal transports in statistical manifolds, Analytic solutions for the approximated 1-D Monge-Kantorovich mass transfer problems, \{Euclidean, metric, and Wasserstein\} gradient flows: an overview, The existence of geodesics in Wasserstein spaces over path groups and loop groups, When is multidimensional screening a convex program?, Convexity and multi-dimensional screening for spaces with different dimensions, Bayesian inference with optimal maps, The fluid dynamic approach to equidistribution methods for grid adaptation, A description of transport cost for signed measures, On the \(n\)-coupling problem, Existence of optimal transport maps for crystalline norms, Note on the Fenchel transform in the Heisenberg group, Optimal vector quantization in terms of Wasserstein distance, Free boundaries in optimal transport and Monge-Ampère obstacle problems, Transportation of measure, Young diagrams and random matrices, On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions, Continuity, curvature, and the general covariance of optimal transportation, Inhomogeneous Hopf-Oleĭnik lemma and regularity of semiconvex supersolutions via new barriers for the Pucci extremal operators, Extremal dependence concepts, Towards a simultaneous Skorohod theorem, An algorithm to approximate the optimal expected inner product of two vectors with given marginals, A new class of transport distances between measures, Optimal and better transport plans, A comparison principle for Hamilton-Jacobi equations related to controlled gradient flows in infinite dimensions, A theorem of stochastic representation related to Monge-Kantorovich problem, Existence and uniqueness of a measure-preserving optimal mapping in a general Monge-Kantorovich problem, Multivariate comonotonicity, The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation, Constructing a relativistic heat flow by transport time steps, Monge problem for \(n\) probabilities, Full characterization of optimal transport plans for concave costs, Invariance properties of the Monge-Kantorovich mass transport problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal coupling of multivariate distributions and stochastic processes
- On the optimal mapping of distributions
- Note on the optimal transportation of distributions
- On Hoeffding-Fréchet bounds and cyclic monotone relations
- A characterization for the solution of the Monge--Kantorovich mass transference problem
- Notes on the Wasserstein metric in Hilbert spaces
- A characterization of random variables with minimum \(L^ 2\)-distance
- On the structure of singular sets of convex functions
- A convexity principle for interacting gases
- On the monotonicity of optimal transportation plans
- Existence and uniqueness of monotone measure-preserving maps
- On \(c\)-optimal random variables
- Solutions in the large for multi-dimensional, non-linear partial differential equations of first order
- Characterization of the subdifferentials of convex functions
- Duality theorems for marginal problems
- The Monge–Kantorovich Mass Transference Problem and Its Stochastic Applications
- Polar factorization and monotone rearrangement of vector‐valued functions
- The Regularity of Mappings with a Convex Potential
- An Extension of Duality-Stability Relations to Nonconvex Optimization Problems
- Differential equations methods for the Monge-Kantorovich mass transfer problem
- Exact solutions to the transportation problem on the line
- Optimal solutions of multivariate coupling problems
- Integer programming and convex analysis: Intersection cuts from outer polars