New article ideas

Below, you can find a list of new article ideas and suggested references. (Feel free to incorporate additional references! Please list all references you use at the bottom of your article.) If you choose to write about one of these ideas, remove it from the list below and create a new link on the main page.

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The Optimal Transport Problem

Unless otherwise specified, all topics are for general cost functions c(x,y).

• Monge Problem; Villani (3-4, 6-9), Santambrogio (xiv-xvii,1-9)
• Kantorovich Problem; Villani (1-3, 6-9), Santambrogio (xv-xvii,1-9)
• Kantorovich Dual Problem (for general costs); Villani (17-21), Santambrogio (9-16)
• Kantorovich Dual Problem (for $c(x,y)=d(x,y)$ where $d$ is a metric); Villani (34)
• Kantorovich Dual Problem (for $c(x,y)=d(x,y)^{2}$ where $d$ is a metric); Santambrogio (16-18)
• Optimal Transport and the Monge Ampère equation; Santambrogio (xvi, 54-57)
• Narrow Convergence: Prokhorov and Portmanteau Theorems (Katy will add refs)

Numerical Methods for Optimal Transport

• Discrete Optimal Transport; Villani (5), Santambrogio (235-237)
• Auction Algorithm; Santambrogio (238-240)
• Entropic Regularization; Santambrogio (240-241)
• Semidiscrete Optimal Transport (for $c(x,y)=|x-y|^{2}$); Santambrogio (242-248)