Optimal Transport Wiki: Difference between revisions
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== The optimal transportation problem == | == The optimal transportation problem == | ||
* [[Monge Problem]] | * [[Monge Problem]] | ||
* [[Monge Problem(revised)]] | |||
* [[Kantorovich Problem]] | * [[Kantorovich Problem]] | ||
* [[Optimal Transport in One Dimension]] | * [[Optimal Transport in One Dimension]] | ||
* [[Kantorovich Dual Problem (for general costs)]] | * [[Kantorovich Dual Problem (for general costs)]] | ||
* [[Kantorovich Dual Problem (for c(x,y) = d(x,y)^2 where d is a metric)]] | * [[Kantorovich Dual Problem (for c(x,y) = d(x,y)^2 where d is a metric)]] | ||
* [[Regularity of Optimal Transport Maps and the Monge-Ampére Equation]] | * [[Regularity of Optimal Transport Maps and the Monge-Ampére Equation on Riemannian Manifolds]] | ||
* [[Wasserstein metric]] | * [[1-Wasserstein metric and generalizations]] | ||
* [[Optimal Transport and Ricci curvature]] | * [[Optimal Transport and Ricci curvature]] | ||
| Line 44: | Line 44: | ||
* [[The Moreau-Yosida Regularization]] | * [[The Moreau-Yosida Regularization]] | ||
* [[Gradient flows in Hilbert spaces]] | * [[Gradient flows in Hilbert spaces]] | ||
* [[The continuity equation]] | * [[The continuity equation and Benamour Brenier formula]] | ||
* [[Isoperimetric inequality and OMT]] | * [[Isoperimetric inequality and OMT]] | ||
==Applications of Optimal Transport== | ==Applications of Optimal Transport== | ||
Latest revision as of 03:58, 17 March 2022
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The optimal transportation problem
- Monge Problem
- Monge Problem(revised)
- Kantorovich Problem
- Optimal Transport in One Dimension
- Kantorovich Dual Problem (for general costs)
- Kantorovich Dual Problem (for c(x,y) = d(x,y)^2 where d is a metric)
- Regularity of Optimal Transport Maps and the Monge-Ampére Equation on Riemannian Manifolds
- 1-Wasserstein metric and generalizations
- Optimal Transport and Ricci curvature
Variants of the optimal transport problem
- Martingale optimal transport and mathematical finance; Santambrogio (51-53); [1]
- Wasserstein barycenters and applications in image processing
The 2-Wasserstein Metric
- Geodesics and generalized geodesics
- Formal Riemannian Structure of the Wasserstein metric
- Asymptotic equivalence of W_2 and H^-1
Numerical methods for optimal transport
- Discrete Optimal Transport
- Auction Algorithm
- Semidiscrete Optimal Transport
- Sinkhorn's Algorithm
- Sliced Wasserstein Distance
Mathematical foundations
- Dual space of C_0(x) vs C_b(x)
- Convergence of Measures and Metrizability
- Fenchel-Moreau and Primal/Dual Optimization Problems
- Fenchel-Rockafellar and Linear Programming
- The Moreau-Yosida Regularization
- Gradient flows in Hilbert spaces
- The continuity equation and Benamour Brenier formula
- Isoperimetric inequality and OMT