Optimization

This post covers the fundamental theorem of OT related to Brenier's theorem and strong duality of the OT problem defining \(2\)-Wasserstein distances.

This post is about the basics of optimal transport (OT) problems and the definition and properties of Wasserstein distances as a special OT problem instance.

This is an introduction to my long post series on Optimal Transport and Wasserstein Gradient Flows!

We study the Asplund decomposition of maximal monotone operators into (i) a convex subdifferential part and (ii) an acyclic operator, a monotone operator with a minimal affine subdifferential component.