Optimal Transport Wiki
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The optimal transportation problem
- Monge Problem
- Kantorovich Problem
- Optimal Transport in One Dimension
- Kantorovich Dual Problem (for general costs)
- Kantorivich Dual Problem with Quadratic Cost
- 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
- Wasserstein-like Metrics on Graphs
- Hellinger-Kantorovich Distance
- Continuous time martingale OT and Skorohod Embedding
- Schrodinger Bridge Problem
Numerical methods for optimal transport
Optimal transport and statistics
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
- Analysis in metric spaces
- Gradient flows in metric spaces