Talk:Discrete Optimal Transport

Statement of the Discrete Problems

• Maybe instead of ``Then any transport plan`` write ``Then any transport plan is of the form... for come choiceof nonnegative weights gij
• Explain heuristically that the transport plan encodes how to rearrange mu to look like nu
• Maybe instead of ``(if it charged anything...``, make this its own sentence and write ``To see this, note that if it charged anything
• Perhaps somethign like ``For SIMPLICITY of notion``
• Before getting into the notation, explain that c(x,y) denotes the cost function (and if you want you can mention the special case of $|x-y|^{2}$)
• The last sentence is great. Consider tweaking it and making it the first sentence of this section. Perhaps ``We now describe the discrete framework. Essentially, we do this by replacing the space... vectors and matrices. In particular, we suppose that mu = sum...``