Talk:Kantorovich Problem

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)