Talk:Kantorovich Problem

Beginning

• Instead of ``The Kantorovich's ot problem``, just ``Kantorovich's ot problem``
• ``Leonid Kantorovich, the founder of modern optimization, who was awarded a Nobel...'
• Change the phrase ``Leonid Kantorovich`` to a link to his wikipedia page
• Add a link to Nobel prize: [[1]]

Introduction

• ``beside THE Monge Problem``
• change the phrase ``Monge Problem`` to a link to the OT wiki page.
• While everything you say in the introduction is correct, it seems a little early to get into this level of technicality. Why not you move this section to the bottom and rename it ``Comparison to Monge Problem``?
• Instead, your introduction can give an heuristic interpretation of the problem, in terms of ``moving around piles of dirt``, which would be understandable to a non-mathematician. You can end the introduction with statement of Kantorovich's OT problem, rather than having this in its own separate section.
• What are $X,Y,{\mathcal {P}}(X),{\mathcal {P}}(Y)$
• Define $\Pi (\mu ,\nu )$
• Define $c(x,y)$

Shipping problem

• It is officially called ``The shipper's problem``
• Cite Villani's Section 1.1.3 and attribute the interpretation to Caffarelli
• This should appear beneath the statement of Kantorovich's Dual Problem. It should be explained how this offers a heuristic interpretation of the dual problem.

Kantorovich Duality Statement

• Change name of section to just ``Kantorovich Duality
• It is not needed to state Kantorovich's problem again

References

• There is an error in the references