8 Weak Monge–Ampère solutions of the semi-discrete optimal transportation problem
Jean-David Benamou, INRIA, Domaine de Voluceau, BP 153 le Chesnay Cedex, France, email@example.com
Brittany D. Froese, Department of Mathematical Sciences, New Jersey Institue of Technology, Newark, NJ 07102, firstname.lastname@example.org
Abstract: We consider the Monge-Kantorovich optimal transportation (OT) problem between two measures, one of which is a weighted sum of Diracs. This problem is traditionally solved using geometric methods based on the computation of Laguerre cells. We review the duality between Brenier/Pogorelov weak solutions and the classical Aleksandrov measure formulation. It is well known that the OT ...