[SCIP] Infeasibility detected by scip

[Stefan Vigerske]

Hi,

if the solution given by Bonmin is feasible, then the instance isn't 
infeasible.
It's probably not the best choice that SCIP says "infeasible" here. What 
it meant to say is that there is no feasible solution where also 
intermediate expressions in your nonlinear function have a value within 
SCIP's range for finite values ([-1e20,1e20]).

There are intermediate expressions like 
exp(((-27.2434)*(<t_x0>+(-10.5675)))) with t_x0 being in [0,1]. When 
SCIP computes a range for this expression, it computes an interval of 
[287.9,315.1] for the argument of exp(). The interval for 
exp([287.9,315.1]) is then beyond SCIP's value for "infinity" (1e20). 
Because this would be a problem for the solution algorithm of SCIP, 
e.g., we couldn't replace expression 
exp(((-27.2434)*(<t_x0>+(-10.5675)))) by an auxiliary variable, SCIP 
decides, a bit lazily, to claim the problem to be infeasible, even 
though the value for the function that contains 
exp(((-27.2434)*(<t_x0>+(-10.5675)))) may actually be within 
[-1e20,1e20] (I saw some pow(...,-1) around it).

There is an option to increase the value for infinity from 1e20 up to 
1e98, but that still wouldn't be sufficient here (exp()'s are beyond 1e113).

For Bonmin, all this is not a problem. It doesn't take the functions 
apart. As long as exp() doesn't actually overflow (which would be around 
1e308), it can evaluate and differentiate the objective and constraints 
and that is all that it needs.
For global solvers, the range of intermediate expressions play a much 
larger role. I don't think there is some magic switch or small change to 
allow SCIP to handle this instance.

The explanation for SCIP's behavior above may apply to 
https://github.com/coin-or/Couenne/issues/61 as well. It sounds like 
that could have been about a similar instance.

Stefan

On 04/07/2023 09:18, Luca Mencarelli wrote:
> Dear Scip community,
> 
> I’m working on non-convex MINLPs and I’m using scip to solve my instances.
> In particular I found this .nl instance which is declared infeasible by scip, but can be actually (locally) solved by bonmin.
> I would ask you if you have any idea of the feasibility problem.
> 
> Thanks very much. Best regards,
> Luca
> 
> 
> 
> 
> 
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