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How to linearize the bilinear constraint $z=xcdot y$ with binary $y$? [closed]
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I would like to linearize the quadratic constraint $$z=xcdot y$$ where $y in 0,1$ is a binary variable and $x in [0,U] cap mathbb Z$ is a bounded integer.
optimization linear-programming integer-programming linearization
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
asked Aug 1 at 11:23
Hang Wu
658
closed as off-topic by John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh Aug 2 at 11:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh
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up vote
0
down vote
favorite
I would like to linearize the quadratic constraint $$z=xcdot y$$ where $y in 0,1$ is a binary variable and $x in [0,U] cap mathbb Z$ is a bounded integer.
optimization linear-programming integer-programming linearization
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
asked Aug 1 at 11:23
Hang Wu
658
closed as off-topic by John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh Aug 2 at 11:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh
$y$ equals $0$ or $1$.
– Hang Wu
Aug 2 at 14:58
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I would like to linearize the quadratic constraint $$z=xcdot y$$ where $y in 0,1$ is a binary variable and $x in [0,U] cap mathbb Z$ is a bounded integer.
optimization linear-programming integer-programming linearization
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
asked Aug 1 at 11:23
Hang Wu
658
I would like to linearize the quadratic constraint $$z=xcdot y$$ where $y in 0,1$ is a binary variable and $x in [0,U] cap mathbb Z$ is a bounded integer.
optimization linear-programming integer-programming linearization
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
asked Aug 1 at 11:23
Hang Wu
658
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
edited Aug 2 at 15:03
Rodrigo de Azevedo
12.6k41751
12.6k41751
asked Aug 1 at 11:23
Hang Wu
658
asked Aug 1 at 11:23
Hang Wu
658
asked Aug 1 at 11:23
Hang Wu
658
658
closed as off-topic by John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh Aug 2 at 11:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh
closed as off-topic by John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh Aug 2 at 11:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Xander Henderson, Mostafa Ayaz, amWhy, Shailesh
$y$ equals $0$ or $1$.
– Hang Wu
Aug 2 at 14:58
add a comment |Â
$y$ equals $0$ or $1$.
– Hang Wu
Aug 2 at 14:58
$y$ equals $0$ or $1$.
– Hang Wu
Aug 2 at 14:58
$y$ equals $0$ or $1$.
– Hang Wu
Aug 2 at 14:58
add a comment |Â
1 Answer
1
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$$
begincases
z leq Uy \
z leq x \
z geq x - U(1-y) \
z geq 0
endcases
$$
if $y=0$ these constraints force $z=0$ while for $y=1$ you get $z=x$.
answered Aug 1 at 13:13
LinAlg
5,4111319
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
$$
begincases
z leq Uy \
z leq x \
z geq x - U(1-y) \
z geq 0
endcases
$$
if $y=0$ these constraints force $z=0$ while for $y=1$ you get $z=x$.
answered Aug 1 at 13:13
LinAlg
5,4111319
add a comment |Â
up vote
2
down vote
$$
begincases
z leq Uy \
z leq x \
z geq x - U(1-y) \
z geq 0
endcases
$$
if $y=0$ these constraints force $z=0$ while for $y=1$ you get $z=x$.
answered Aug 1 at 13:13
LinAlg
5,4111319
add a comment |Â
up vote
2
down vote
up vote
2
down vote
$$
begincases
z leq Uy \
z leq x \
z geq x - U(1-y) \
z geq 0
endcases
$$
if $y=0$ these constraints force $z=0$ while for $y=1$ you get $z=x$.
answered Aug 1 at 13:13
LinAlg
5,4111319
$$
begincases
z leq Uy \
z leq x \
z geq x - U(1-y) \
z geq 0
endcases
$$
if $y=0$ these constraints force $z=0$ while for $y=1$ you get $z=x$.
answered Aug 1 at 13:13
LinAlg
5,4111319
answered Aug 1 at 13:13
LinAlg
5,4111319
answered Aug 1 at 13:13
LinAlg
5,4111319
answered Aug 1 at 13:13
LinAlg
5,4111319
5,4111319
add a comment |Â
add a comment |Â
$y$ equals $0$ or $1$.
– Hang Wu
Aug 2 at 14:58