Asian Journal of Mathematics
Volume 20 (2016)
Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge–Ampère equations
Pages: 383 – 398
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–Ampère equation (DMAE). A link between the discrete optimal transport, the discrete Monge–Ampère equation and the power diagram in computational geometry is established.
Monge–Ampère equation, Minkowski problem, Alexandrov problem, variational, power diagram
2010 Mathematics Subject Classification
Primary 52B55. Secondary 52B11, 65M99.