Talk:Semidiscrete Optimal Transport

Voronoi cells to find weights

• The weights b_j are given. The goal of the algorithm is to find which REGIONS V_\phi(j) in the support of the source measure \mu are sent to each y_j. These regions are determined by the function phi. You want to find a function phi so that b_j = \int_{V_\phi(j)} f(x) dx.

Finding the weights

• As above, the goal is to find phi. The weights are given.
• Cite Merigot for the fact that the energy E(\phi) is concave.
• You may consider either clarifying or removing the last sentence of this section.

Algorithm discussion

• This is a very nice summary. Consider adding some references.