Numerical difficulties with SOCP model or "Unbounded" with BarHomogenous=1

[Enrique Fernández]

Hello,

Gurobi is reporting numerical difficulties with my model and suggesting to use BarHomogeneous=1.

Doing so, Gurobi reports that the model is unbounded.

However, I don't think that's the case.

The model is optimizing a variable and the value of the variable is constrained by two straightforward bounds (v <= 100 and v >= 0).

Could this be a bug?

When setting BarHomogeneous=1, Gurobi does not report numerical difficulties, it simply says that it is unbounded.

Turning Presolve to 0 doesn't change the outcome.

Thanks!

[Sonja Mars]

Hi,

Can you post log files showing the different runs?

Thanks and best regards,
Sonja


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Dr. Sonja Mars
Gurobi Optimization - Technical Support

[Enrique Fernández]

Hi Sonja

Thanks for your reply.

I think I'm running into numerical issues.

As reported earlier, with my original model I get:

- Numerical difficulties with default settings

- Unbounded model result if I use BarHomogeneous=1 (but I'm minimizing a variable that is constrained by lower and upper constant bounds)

Changing one of my model parameters from 0.0001 to 0.01 gives:

- The same numerical difficulties with default settings

- Unfeasible result with BarHomogeneous

I think this is just a very unlucky bad-conditioned problem that happens to be really barely feasible when the parameter is 0.0001 and not feasible increasing that number.

In any case I don't think Gurobi should return "Unbounded" when using BarHomogeneous, but "numerical difficulties".

I've sent both files to support[at]gurobi.com

- gurobi_false_unbounded.mps (with original parameter)

- gurobi_false_unbounded2.mps (with parameter set to 0.01)

Thanks!

Enrique

[Sonja Mars]

Hi Enrique,

Thanks for reporting this and for sharing the models with us. Unfortunately, I was not able to reproduce this. I wasn't able to solve the model at all, I always got "Numerical Trouble" or "Sub-optimal termination".

> I think this is just a very unlucky bad-conditioned problem that happens to be really barely feasible when the parameter is 0.0001 and not feasible increasing that number.

Yes, I think this is the case. And I guess this is also why you get the strange result with "Unbounded". Gurobi is not able to handle this SOCP due to the bad numerics.

I am very sorry that I cannot give you a better answer, but numerics can be tricky. I will send your model to our developers, maybe they can find something to make the code more robust for this case.

Best regards,