[SCIP] Strict Integer Inequalities

[Matthias Walter]

Dear Alexander,

I assume that in your problem description you are using the LP format. 
However, the documentation

https://www.tu-chemnitz.de/mathematik/discrete/manuals/cplex/doc/refman/html/appendixE5.html

states "... <, <=, =<, >, >=, =>, and =. These are interpreted as <=, 
<=, <=, >=, >=, >= and =, respectively". The reason is that linear 
programs (which are used as relaxations for IPs) in general do not allow 
strict inequalities.

Best,
Matthias

On 03.03.22 01:17, Alex Meiburg wrote:
> I noticed that SCIP doesn't seem to like strict inequalities for 
> integers. When it solves
>
> Maximize
> k
> st
> k < 10
> Integer
> k
>
> I get the solution
>
> solution status: optimal solution found
> objective value:                                   10
> k                                                  10 (obj:1)
>
> When of course that's not actually feasible. :) In this case of course 
> it's pretty simple to remedy by replacing "[foo] < N" by "[foo] <= 
> N-1". But that's not always valid, e.g. in the problem
>
> Maximize
> halfK
> st
> halfK < 10
> halfK + halfK = k
> Integer
> k
>
> ... in which case the correct answer is 9.5 (and SCIP think it's 10). 
> I'm using SCIP v7.0.2. Is there any interest in fixing this, or at 
> least, documenting it better...? I skimmed and couldn't find any 
> warnings about not using strict inequalities.
>
> -- Alexander Meiburg
>
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