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* Optimal Transport in One Dimension; Villani (73-78); Santambrogio (59-67) | * Optimal Transport in One Dimension; Villani (73-78); Santambrogio (59-67) | ||
* 1-Wasserstein metric, duality, and measures with unequal mass; [https://arxiv.org/pdf/1910.05105.pdf Piccoli, Rossi, and Tournus ''A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term''] | * 1-Wasserstein metric, duality, and measures with unequal mass; [https://arxiv.org/pdf/1910.05105.pdf Piccoli, Rossi, and Tournus ''A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term''] | ||
* Geodesics and generalized geodesics | |||
==The 2-Wasserstein Metric== | |||
* Geodesics and generalized geodesics; Santambrogio (202-207)<span style="color:red">more refs</span> | |||
* (Displacement) convex functionals in the 2-Wasserstein metric; Santambrogio (249-251,271-276) | |||
==Numerical Methods for Optimal Transport== | ==Numerical Methods for Optimal Transport== | ||
* Semidiscrete Optimal Transport (for <math> c(x,y) = |x-y|^2 </math>); Santambrogio (242-248); Peyré Cuturi (85-89) | * Semidiscrete Optimal Transport (for <math> c(x,y) = |x-y|^2 </math>); Santambrogio (242-248); Peyré Cuturi (85-89) | ||
* Computing OT via Benamou-Brenier; Santambrogio (220-225)<span style="color:red">more refs</span> | |||
==Applications of Optimal Transport== | ==Applications of Optimal Transport== | ||
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==Mathematical Foundations: Optimization== | ==Mathematical Foundations: Optimization== | ||
* Fenchel-Rockafellar and Linear Programming; Brezis (15-17); Rockafellar, ''Variational Analysis'' (505-507) | * Fenchel-Rockafellar and Linear Programming; Brezis (15-17); Rockafellar, ''Variational Analysis'' (505-507) | ||
==Mathematical Foundations: Differential Equations== | |||
* Gradient flows in metric spaces; Santambrogio (285-290) | |||
Revision as of 20:52, 25 May 2020
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
- Optimal Transport in One Dimension; Villani (73-78); Santambrogio (59-67)
- 1-Wasserstein metric, duality, and measures with unequal mass; Piccoli, Rossi, and Tournus A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term
The 2-Wasserstein Metric
- Geodesics and generalized geodesics; Santambrogio (202-207)more refs
- (Displacement) convex functionals in the 2-Wasserstein metric; Santambrogio (249-251,271-276)
Numerical Methods for Optimal Transport
- Semidiscrete Optimal Transport (for ); Santambrogio (242-248); Peyré Cuturi (85-89)
- Computing OT via Benamou-Brenier; Santambrogio (220-225)more refs
Applications of Optimal Transport
- Machine Learning Kolouri, et al, Optimal Mass Transport: Signal processing and machine-learning applications
Mathematical Foundations: Functional Analysis
Mathematical Foundations: Optimization
- Fenchel-Rockafellar and Linear Programming; Brezis (15-17); Rockafellar, Variational Analysis (505-507)
Mathematical Foundations: Differential Equations
- Gradient flows in metric spaces; Santambrogio (285-290)