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* [[Formal Riemannian Structure of the Wasserstein metric]] | * [[Formal Riemannian Structure of the Wasserstein metric]] | ||
* [[Asymptotic equivalence of W_2 and H^-1]] | * [[Asymptotic equivalence of W_2 and H^-1]] | ||
* [[2-Wasserstein Metric and Ricci curvature]] | |||
== Numerical methods for optimal transport == | == Numerical methods for optimal transport == | ||
Revision as of 20:30, 10 February 2022
Welcome to the Optimal Transport Wiki!
Here is a list of New article ideas.
Contact Katy Craig if you would like to contribute to this wiki.
The optimal transportation problem
- Monge Problem
- Kantorovich Problem
- Optimal Transport and the Monge Ampère equation
- 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
- 1-Wasserstein metric, duality, and measures with unequal mass
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
- 2-Wasserstein Metric and Ricci curvature
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