[Scip] help : for expressing constraint

[Ambros Gleixner]

Dear Abdelkader Ouali,

SCIP does not provide a constraint handler for this type of equivalence. 
  If you do not want to model it via simple linear big-M constraints, 
then you could use two indicator constraints, see

    http://scip.zib.de/doc/html/cons__indicator_8h.php

For the implication Y == 0 -> Ct Xt != 0 you can use SCIPgetNegatedVar() 
on Y, see

 
http://scip.zib.de/doc/html/scip_8h.php#a94ec8a6bca8e6e621751b4257bf0d4c1

I assume that because Xt are binary, you can express Ct Xt != 0 as a 
linear equality or inequality constraint.

(Because the indicator constraint handler only enforces inequalities, 
maybe you need to indicator constraints to model Y==1 -> Ct Xt == 0 as 
Ct Xt <= 0 and Ct Xt >= 0, if one of them is not globally valid.  In 
this case it may be more efficient to write an your own big-M formulation.)

Best regards,
ambros



Am 16.07.2014 16:52, schrieb Abdelkader Ouali:
> Dear SCIP users,
>
> I have a constraint as follow :
>
> Y=1 <-> Ct Xt = 0
> where :
> Y : is binary variable
> Xt : is binary set of binary variables
> Ct : is constant (coefficient) associated to each Xt
> I had some problems to formulate it in SCIP, since there is equivalence
> between to linear constraints
>
> Can you give some help to implement it ?
>
> ---
> A. Ouali
>
>
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-- 
____________________________________________________________
Ambros M. Gleixner
Zuse Institute Berlin - Matheon - Berlin Mathematical School
http://www.zib.de/gleixner