Originally posted by: imen1401

Hello,

can someone help me to change the constraint : Abs(x) > a in order to have a linear constraint ?
#DecisionOptimization
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Originally posted by: Didier Vidal

Hi,

I moved this question to mathematical programming where I think it will find more readers able to propose their solutions.

Regards.

Didier Vidal.
#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

> imen1401 wrote:
> Hello,
>
> can someone help me to change the constraint : Abs(x) > a in order to have a linear constraint ?

First, you cannot have a strict inequality in a math program, only a weak one (>= here). Second, you will need a priori upper and lower bounds U, L for x (so that L <= x <= U is known to hold). Third, you will need to introduce a binary variable z. Then add the two constraints

x >= a*z + L*(1-z)
x <= U*z - a*(1-z).

/Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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Originally posted by: imen1401

Hello,

I am very grateful to you for your help Paul Rubin. Thanks to your constraints my model is now linear.

Thank you.
Best regards.
Imen.
#DecisionOptimization
#MathematicalProgramming-General