Talk:Optimal Transport and the Monge Ampère equation: Difference between revisions
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==Beginning== | ==Beginning== | ||
* Cite specific pages where Santambrogio discusses Monge Ampere, since this is only a small part of that chapter | * Cite specific pages where Santambrogio discusses Monge Ampere, since this is only a small part of that chapter | ||
* | * The explanation of the relationship to optimal transport is a little confusing. It might be better to explain what a transport map is (perhaps linking to the page on the Monge Problem on the OT wiki) and say something along the lines of ``under sufficient regularity assumptions on the measures mu and nu, the condition that a transport map pushes forward mu to nu can be equivalently formulated in terms of the transport map solving a type of Monge-Ampere equation`` | ||
* The only time that we need the cost to be quadratic is to reduce to the case that the transport map is given by the gradient of a convex function. Maybe it's best to save explaining this technicality to the next section. | |||
Revision as of 22:37, 13 May 2020
Beginning
- Cite specific pages where Santambrogio discusses Monge Ampere, since this is only a small part of that chapter
- The explanation of the relationship to optimal transport is a little confusing. It might be better to explain what a transport map is (perhaps linking to the page on the Monge Problem on the OT wiki) and say something along the lines of ``under sufficient regularity assumptions on the measures mu and nu, the condition that a transport map pushes forward mu to nu can be equivalently formulated in terms of the transport map solving a type of Monge-Ampere equation``
- The only time that we need the cost to be quadratic is to reduce to the case that the transport map is given by the gradient of a convex function. Maybe it's best to save explaining this technicality to the next section.