Optimal Transport Wiki

Welcome to the Optimal Transport Wiki!

Contributors wanted!

Do you want to help others learn about optimal transport? Do you need a concrete goal to motivate yourself to learn about a new topic? Please consider becoming a contributor to our wiki!

Your contributions will be gratefully recognized in footers of each page. Please contact Katy Craig to receive an account.

Here is a list of New article ideas.

The optimal transportation problem

• Monge Problem
• Kantorovich Problem
• Optimal Transport and the Monge Ampère equation
• Kantorovich Dual Problem (for general costs)
• Kantorovich Dual Problem (for c(x,y) = d(x,y)^2 where d is a metric)

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

Applications of Optimal Transport

• Machine Learning

Other

• Distraction Recommendations
• Nonlocal Equations Wiki
• Proteopedia
• Quantum Information Wiki