[SCIP] Undeclared Variables Used in the Constraints

[Ambros Gleixner]

Hi Samuel,

This depends on the objective function coefficient of the variable in 
relation to the coefficient of the variable in the constraint and the 
sides of the constraint.

Say the objective coefficient is nonnegative and the constraint is a <= 
constraint.  Decreasing the variable always improves the objective or 
leaves it unchanged.

Now if the constraint coefficient is positive, then SCIP will fix the 
variable at minus infinity, according to the fact that one can always 
choose a sufficiently small, finite value to satisfy the constraint.

If the constraint coefficient is negative, then it is best to set the 
variable such that the inequality is tight.  This means performing a 
multi-aggregation and is described in detail in Algorithm 10.4 of Tobias 
Achterberg's thesis

http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11129

To look at the code, see method dualPresolve() in cons_linear.c.

Hope that helps.

Best,
Ambros





Am 14.09.20 um 23:07 schrieb Samuel Jiménez Gil:
> Hi all,
> Hope you are well. I've done quite a few experiments trying to 
> understand this question but I don't manage to understand the rationale.
> 
> Do you know what SCIP does when you add an arbitrary constraint 
> containing a variable which was not declared (free variable), and thus 
> no bounds were provided?
> 
> Example, (t_0 not declared):
> 
> Minimize
> 0
> Subject To
>   c1: i_0 + i_1 > 11
>   c2: i_0 - 2 i_1 > -1
>   c3: t_0 > 40
> Bounds
>   0 <= i_0 <= 1000
>   0 <= i_1 <= 1000
> End
> 
> According to what I've seen t_0 could have any value and is ocassionally 
> replaced by one of the declared variables.
> 
> Many thanks in advance.
> 
> Samuel.
> Ph.D Candidate.
> 
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-- 
Ambros Gleixner, Research Group Mathematical Optimization Methods at 
Zuse Institute Berlin, http://www.zib.de/gleixner