Name for Monge-Kantorovich transportation problem variant with unequal total mass
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I'm interested in a variant of the transportation problem and cannot find a reference for the problem I'm thinking of.
In the original Monge-Kantorovich problem about continuous transport, the total mass of $m$ objects are to be moved to the same mass of destinations. Assuming a quadratic euclidean distance cost, the solution is well known and has some nice properties.
What happens if the total masses of each side are different? e.g., if mass $1$ objects should be moved to total mass of $x$ destinations, $xneq 1$? So if $x<1$ some of the objects cannot be moved because of this capacity constraint. On the other hand, if $x>1$, what would be the optimal transport? (assuming quadratic costs)
Anyone familiar with this variant? I can't find a reference that deals with this problem..
optimal-transport
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
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add a comment |
$begingroup$
I'm interested in a variant of the transportation problem and cannot find a reference for the problem I'm thinking of.
In the original Monge-Kantorovich problem about continuous transport, the total mass of $m$ objects are to be moved to the same mass of destinations. Assuming a quadratic euclidean distance cost, the solution is well known and has some nice properties.
What happens if the total masses of each side are different? e.g., if mass $1$ objects should be moved to total mass of $x$ destinations, $xneq 1$? So if $x<1$ some of the objects cannot be moved because of this capacity constraint. On the other hand, if $x>1$, what would be the optimal transport? (assuming quadratic costs)
Anyone familiar with this variant? I can't find a reference that deals with this problem..
optimal-transport
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
$endgroup$
add a comment |
$begingroup$
I'm interested in a variant of the transportation problem and cannot find a reference for the problem I'm thinking of.
In the original Monge-Kantorovich problem about continuous transport, the total mass of $m$ objects are to be moved to the same mass of destinations. Assuming a quadratic euclidean distance cost, the solution is well known and has some nice properties.
What happens if the total masses of each side are different? e.g., if mass $1$ objects should be moved to total mass of $x$ destinations, $xneq 1$? So if $x<1$ some of the objects cannot be moved because of this capacity constraint. On the other hand, if $x>1$, what would be the optimal transport? (assuming quadratic costs)
Anyone familiar with this variant? I can't find a reference that deals with this problem..
optimal-transport
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
$endgroup$
I'm interested in a variant of the transportation problem and cannot find a reference for the problem I'm thinking of.
In the original Monge-Kantorovich problem about continuous transport, the total mass of $m$ objects are to be moved to the same mass of destinations. Assuming a quadratic euclidean distance cost, the solution is well known and has some nice properties.
What happens if the total masses of each side are different? e.g., if mass $1$ objects should be moved to total mass of $x$ destinations, $xneq 1$? So if $x<1$ some of the objects cannot be moved because of this capacity constraint. On the other hand, if $x>1$, what would be the optimal transport? (assuming quadratic costs)
Anyone familiar with this variant? I can't find a reference that deals with this problem..
optimal-transport
optimal-transport
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
asked Dec 13 '18 at 15:42
GreenteamaniacGreenteamaniac
345
345
add a comment |
add a comment |
1 Answer
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This variant of the optimal transport problem is called "optimal partial transport".
See here and here.
answered Jan 30 at 10:59
MOMOMOMO
717312
$endgroup$
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
oldest
votes
active
oldest
votes
$begingroup$
This variant of the optimal transport problem is called "optimal partial transport".
See here and here.
answered Jan 30 at 10:59
MOMOMOMO
717312
$endgroup$
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
add a comment |
$begingroup$
This variant of the optimal transport problem is called "optimal partial transport".
See here and here.
answered Jan 30 at 10:59
MOMOMOMO
717312
$endgroup$
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
add a comment |
$begingroup$
This variant of the optimal transport problem is called "optimal partial transport".
See here and here.
answered Jan 30 at 10:59
MOMOMOMO
717312
$endgroup$
This variant of the optimal transport problem is called "optimal partial transport".
See here and here.
answered Jan 30 at 10:59
MOMOMOMO
717312
answered Jan 30 at 10:59
MOMOMOMO
717312
answered Jan 30 at 10:59
MOMOMOMO
717312
answered Jan 30 at 10:59
MOMOMOMO
717312
717312
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
add a comment |
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
$begingroup$
Thanks so much!
$endgroup$
– Greenteamaniac
Feb 1 at 1:28
add a comment |
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