Absolute value as a linear programming constraint?

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Mike Vukovich
Mike Vukovich 2013-6-21
编辑： Matt J 2020-4-8
Suppose I want to use absolute values in a constraint equation for linear or mixed integer programming - i.e. suppose I need one of the form abs(x1) + abs(x2) <= 1.
How would I incorporate this in the constraint matrix in MATLAB?

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回答（1 个）

Matt J
Matt J 2013-6-22
编辑：Matt J 2013-6-22
abs(x1+x2)<=1
is equivalent to the constraints
x1+x2<=1
-(x1+x2)<=1
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James Tursa
James Tursa 2020-4-8
编辑：James Tursa 2020-4-8
Correct. This constraint abs(x1) + abs(x2) <= 1 is actually inside a diamond with vertices at (1,0), (0,1), (-1,0), and (0,-1). So there would be four inequality constraints involved for the four line segments, not just two.
Matt J
Matt J 2020-4-8
编辑：Matt J 2020-4-8
The original question was how to code abs(x1)+abs(x2)<=1 as a constraint.
I suspect the original question was abs(x1+x2) and was later edited....
However, abs(x1) + abs(x2) <= 1 can be represented by 4 inequality constraints, as James says:
[1 1 * [x1;x2] <=[1;1;1;1]
1 -1
-1 1
-1 -1]

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