Talk:Kantorovich Problem: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
==Introduction== | ==Introduction== | ||
* `` | * Great picture! | ||
* Instead of ``The Kantorovich problem allows a non-empty minimization set, a convex constraint set,`` consider ``in the Kantorovich problem, the constraint set is convex and nonempty``. | |||
* Consider referencing the more specific page for ``dual``: https://en.wikipedia.org/wiki/Dual_linear_program | |||
* | * More specifically ``it is a linear minimization problem with LINEAR constraints`` | ||
* Consider removing this discussion of the shipping problem and referring instead to the OT wiki article on the Kantorovich Dual Problem | |||
* | |||
* | |||
== | ==Kantorovich Optimal Transport Problem== | ||
* | * The problem isn't stated correctly -- it is a minimization problem, right? | ||
* | * Remove the last phrase ``or equivalently Linfty dmu Linfty d nu`` since this is already implied by saying it holds for \phi and \psi in L1 | ||
* The Remarks section is a direct paraphrase of Villani. Unfortunately, it doesn't make sense as written and could be considered copyright infringement. Please remove it. | |||
==Kantorovich Duality | ==Kantorovich Duality== | ||
* | * Please remove this section and instead refer to the OT wiki article on the Kantorovich Dual | ||
==References== | ==References== | ||
* | * Villani (1-3, 6-9), Santambrogio (xv-xvii,1-9) | ||
Latest revision as of 17:09, 27 May 2020
Introduction
- Great picture!
- Instead of ``The Kantorovich problem allows a non-empty minimization set, a convex constraint set,`` consider ``in the Kantorovich problem, the constraint set is convex and nonempty``.
- Consider referencing the more specific page for ``dual``: https://en.wikipedia.org/wiki/Dual_linear_program
- More specifically ``it is a linear minimization problem with LINEAR constraints``
- Consider removing this discussion of the shipping problem and referring instead to the OT wiki article on the Kantorovich Dual Problem
Kantorovich Optimal Transport Problem
- The problem isn't stated correctly -- it is a minimization problem, right?
- Remove the last phrase ``or equivalently Linfty dmu Linfty d nu`` since this is already implied by saying it holds for \phi and \psi in L1
- The Remarks section is a direct paraphrase of Villani. Unfortunately, it doesn't make sense as written and could be considered copyright infringement. Please remove it.
Kantorovich Duality
- Please remove this section and instead refer to the OT wiki article on the Kantorovich Dual
References
- Villani (1-3, 6-9), Santambrogio (xv-xvii,1-9)