Fetching the paper…
Reading the bibliography…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e.
Uber die umkehrung der naturgesetze
E. Schrodinger · 1931
Earlier work this paper cites.
On a least squares adjustment of a sampled frequency table when the expected marginal totals are known
W. E. Deming and F. F. Stephan · 1940
Earlier work this paper cites.
On the transfer of masses (in russian)
L. Kantorovich · 1942
Earlier work this paper cites.
A relationship between arbitrary positive matrices and doubly stochastic matrices
R. Sinkhorn · 1964
Earlier work this paper cites.
The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
L. M. Bregman · 1967
Earlier work this paper cites.
Diagonal equivalence to matrices with prescribed row and column sums
R. Sinkhorn · 1967
Earlier work this paper cites.
Concerning nonnegative matrices and doubly stochastic matrices
R. Sinkhorn and P . Knopp · 1967
Earlier work this paper cites.
On the behavior of the fundamental solution of the heat equation with variable coefficients
S. R. S. Varadhan · 1967
Earlier work this paper cites.
I I -divergence geometry of probability distributions and minimization problems
I. Csiszár · 1975
Earlier work this paper cites.
Introduction to Numerical Linear Algebra and Optimisation
P. G. Ciarlet · 1982
Earlier work this paper cites.
An iterative procedure for obtaining I I -projections onto the intersection of convex sets
R. L. Dykstra · 1985
Earlier work this paper cites.
The least action principle and the related concept of generalized flows for incompressible perfect fluids
Y. Brenier · 1990
Earlier work this paper cites.
Recursively implementing the Gaussian and its derivatives
R. Deriche · 1993
Earlier work this paper cites.
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
J. Eckstein · 1993
Earlier work this paper cites.
Interior-point polynomial algorithms in convex programming
Y. Nesterov, A. Nemirovskii, and Y. Ye · 1994
Earlier work this paper cites.
Proximal minimization methods with generalized Bregman functions
K.C. Kiwiel · 1997
Earlier work this paper cites.
The Dykstra algorithm with Bregman projections
Y. Censor and S. Reich · 1998
Earlier work this paper cites.
The variational formulation of the Fokker-Planck equation
R. Jordan, D. Kinderlehrer, and O. Otto · 1998
Earlier work this paper cites.
Closedness of sum spaces and the generalized Schrodinger problem
L. Ruschendorf and W. Thomsen · 1998
Earlier work this paper cites.
Anisotropic Diffusion in Image Processing
J. Weickert · 1998
Earlier work this paper cites.
Dykstra’s algorithm as the nonlinear extension of Bregman’s optimization method
L.M. Bregman, Y. Censor, and S. Reich · 1999
Earlier work this paper cites.
Approximation of parabolic equations using the Wasserstein metric
D. Kinderlehrer and N. J Walkington · 1999
Earlier work this paper cites.
Level Sets Methods and Fast Marching Methods
J.A. Sethian · 1999
Earlier work this paper cites.
Dykstra’s algorithm with Bregman projections: a convergence proof
H. H. Bauschke and A. S. Lewis · 2000
Cited alongside, same era.
A computational fluid mechanics solution of the Monge-Kantorovich mass transfer problem
J.-D. Benamou and Y. Brenier · 2000
Cited alongside, same era.
The earth mover’s distance as a metric for image retrieval
Y. Rubner, C. Tomasi, and L.J. Guibas · 2000
Cited alongside, same era.
An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions
M. V. Solodov and B. F. Svaiter · 2000
Cited alongside, same era.
The geometry of dissipative evolution equations: the porous medium equation
F. Otto · 2001
Cited alongside, same era.
Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
Global convergence of a non-convex douglas-rachford iteration
A. Artacho, Borwein F. J., and J. M · 2012
Later among the works it cites.
Consistent estimation of a population barycenter in the Wasserstein space
J. Bigot and T. Klein · 2012
Later among the works it cites.
Optimal transport and Cournot-Nash equilibria
A. Blanchet and G. Carlier · 2012
Later among the works it cites.
Regularised regression and density estimation based on optimal transport
M. Burger, M. Franeka, and C-B. Schonlieb · 2012
Later among the works it cites.
On the local structure of optimal measures in the multi-marginal optimal transportation problem
B. Pass · 2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
M. Agueh · 2002
Cited alongside, same era.
Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization
H. H. Bauschke, P. L. Combettes, and D. R. Luke · 2002
Cited alongside, same era.
Monge-Ampere-Kantorovitch (MAK) reconstruction of the early universe
U. Frisch, S. Matarrese, R. Mohayaee, and A. Sobolevski · 2002
Cited alongside, same era.
Topics in Optimal Transportation
C. Villani · 2003
Cited alongside, same era.
Gradient flows: in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2006
Cited alongside, same era.
Direct Methods for Sparse Linear Systems
T. A. Davis · 2006
Cited alongside, same era.
A Dykstra-like algorithm for two monotone operators
H. H. Bauschke and P. L. Combettes · 2008
Cited alongside, same era.
One-dimensional numerical algorithms for gradient flows in the p p -Wasserstein spaces
M. Agueh and M. Bowles · 2013
Later among the works it cites.
Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the eady problem
C.J. Budd, M.J.P. Cullen, and E.J. Walsh · 2013
Later among the works it cites.
Geodesics in heat: A new approach to computing distance based on heat flow
K. Crane, C. Weischedel, and M. Wardetzky · 2013
Later among the works it cites.
Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
Later among the works it cites.
Insights into capacity constrained optimal transport
K. Jonathan and R. J. McCann · 2013
Later among the works it cites.
Discretization of functionals involving the Monge-Ampère operator
J-D. Benamou, G. Carlier, Q. Mérigot, and E. Oudet · 2014
Later among the works it cites.
On the ergodic convergence rates of a first-order primal-dual algorithm
A. Chambolle and T. Pock · 2014
Later among the works it cites.
Fast computation of Wasserstein barycenters
M. Cuturi and A. Doucet · 2014
Later among the works it cites.
Sparse non-negative stencils for anisotropic diffusion
J. Fehrenbach and J-M. Mirebeau · 2014
Later among the works it cites.
A survey of the Schrodinger problem and some of its connections with optimal transport
C. Leonard · 2014
Later among the works it cites.
Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation
D. Matthes and H. Osberger · 2014
Later among the works it cites.
Optimal transport with proximal splitting
N. Papadakis, G. Peyré, and E. Oudet · 2014
Later among the works it cites.
Bregman alternating direction method of multipliers
H. Wang and A. Banerjee · 2014
Later among the works it cites.
Synthesizing and mixing stationary Gaussian texture models
G-S. Xia, S. Ferradans, G. Peyré, and J-F. Aujol · 2014
Later among the works it cites.
Iterative bregman projections for regularized transportation problems
J-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré · 2015
Closest in time.
A finite-volume method for nonlinear nonlocal equations with a gradient flow structure
J. A. Carrillo, A. Chertock, and Y. Huang · 2015
Closest in time.
Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains
J. Solomon, F. de Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas · 2015
Closest in time.