Optimal Transport Wiki
Welcome to the Optimal Transport Wiki!
Here is a list of new article ideas. Here is a list of suggestions of articles to revise
Contact Katy Craig if you would like to contribute to this wiki.
The optimal transportation problem
- Monge Problem
- Kantorovich Problem
- Optimal Transport in One Dimension - will be revised by Yusen
- Kantorovich Dual Problem (for general costs)
- Kantorovich Dual Problem (for \(c(x,y) = d(x,y)^2\) where \(d\) is a metric) - Evan Tufte will revise
- Regularity of Optimal Transport Maps and the Monge-Ampére Equation on Riemannian Manifolds
- 1-Wasserstein metric and generalizations
- Dynamic Optimal Transport
- Optimal Transport and Ricci curvature
The 2-Wasserstein Metric
Variants of the optimal transport problem
- Martingale optimal transport and mathematical finance
- Martingale optimal transport: dynamic formulation
- Wasserstein barycenters and applications in image processing - Charles will revise
- Wasserstein-like Metrics on Graphs
- Hellinger-Kantorovich Distance
- Continuous time martingale OT and Skorohod Embedding
Numerical methods for optimal transport
- Discrete Optimal Transport
- Auction Algorithm
- Semidiscrete Optimal Transport
- Sinkhorn’s Algorithm - Jack Pfaffinger will revise
- Sliced Wasserstein Distance - Arie
- Back and Forth Method
Optimal Transport and Statistics
Wasserstein Gradient Flows
- Probability flow solution of the Fokker–Planck equation - Simone Betteti - Boffi and Vanden-Eijnden 2023
- Bures-Wasserstein Gradient flows
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
- Gaussian Measures
- Gradient flows in metric spaces