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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Jean-David Benamou and Brittany D. Froese

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, jeandavid.benamou@inria.fr

Brittany D. Froese, Department of Mathematical Sciences, New Jersey Institue of Technology, Newark, NJ 07102, bdfroese@njit.edu

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 ...

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