The tag has no wiki summary.

learn more… | top users | synonyms

-1
votes
0answers
19 views

Constructing a family of domains for application of method of continuity in optimal transportation

Anyway can help me about this paper? http://arxiv.org/pdf/math/0601086v4.pdf I want to ask page 20, The author want to construct a family of subdomain for using method of continuity. But I can't ...
0
votes
0answers
23 views

Deterministic Coupling

Let $X=Y=[0,2\pi]$ And $X,\ Y$ has standard Lebesque measure $\mu=\nu$ Definition : Coulping for two spaces is a measure $\pi$ s.t. $$ \pi(A\times Y)= \mu(A),\ \pi(X\times A)=\nu(A) $$ ...
4
votes
1answer
32 views

Why is the shift the optimal plan between $[0,1)$ and $[1,2)$ (with distance-squared cost function)?

Example 1.3 of Optimal and Better Transport Plans reads Consider the task to transport points on the real line (equipped with the Lebesgue measure) from the interval [0, 1) to [1, 2) where the ...
4
votes
0answers
65 views

Spacing nodes by moving the shortest distance possible.

I have a list of N nodes with positions $(x, y)$ each. I want to move each node the shortest possible distance such that every node is placed on the radius $R$ from at least one other node, and is at ...
0
votes
0answers
133 views

Transportation Problem - Linear Algebra

Say we have a standard transportation problem with supply and demand vectors S = [50, 60] and d = [20, 50, 40] and the cost matrix C =  R1) 4 3 5 R2) 3 6 2  The minimum cost method provides a way ...
4
votes
0answers
79 views

Cyclically monotone sets on four points

A subset of $\mathcal{X} \times \mathcal{Y} \subset \mathbb{R}^d \times \mathbb{R}^d$ is cyclically monotone if $\sum_{i=1}^n \langle x_i,y_i\rangle \ge \sum_{i=1}^n \langle x_i,y_{i+1}\rangle$, where ...