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In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE).
Extrinsic geometry of convex surfaces. Translated from the Russian by Israel Program for Scientific Translations
A. V. Pogorelov · 1973
Earlier work this paper cites.
Power diagrams: properties, algorithms and applications
F. Aurenhammer · 1987
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Minkowski-type theorems and least-squares clustering
F. Aurenhammer, F. Hoffmann, and B. Aronov · 1998
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Convex analysis and nonlinear optimization. Theory and examples
Jonathan M. Borwein and Ardian S. Lewis · 2000
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Topics in optimal transportation
Cédric Villani · 2003
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Ameobas, monge-ampàre measures, and triangulations of the newton polytope
Mikael Passare and Hans Rullgård · 2004
Cited alongside, same era.
Convex polyhedra Translated from the 1950 Russian edition by N. S. Dairbekov, S. S. Kutateladze and A. B. Sossinsky
A. D. Alexandrov · 2005
Later among the works it cites.
Power diagrams and their applications
D. Siersma and M. van Manen · 2005
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Notions of convexity Reprint of the 1994 edition
Lars Hörmander · 2007
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