Gurobi says unbounded, I think it is infeasible

[Angelos]

Hi,

I am trying to solve the attached linear program using Gurobi.
Gurobi tells me it is unbounded while the problem should be (I think) infeasible.
I am using the C++ interface, but I get the same results with the command line tool.

Note that the first 4 lines of the .lp file are :
*************
Minimize
  epigraph
Subject To
extra: epigraph >= -10000
************************************
Clearly the problem cannot be unbounded, either it is infeasible or it has an optimal value larger or equal to -10000.
(I only have this constraint there for debugging purposes, I suspect the model without this constraint is still infeasible and not unbounded.)

The way I run it from the command line is:

$ gurobi.sh
gurobi> m=read('withextra.lp')
gurobi> setParam('DualReductions',0)
gurobi> m.optimize()

I obtain the output:
Optimize a model with 85 rows, 13 columns and 305 nonzeros
Coefficient statistics:
  Matrix range    [5e-01, 4e+05]
  Objective range [1e+00, 1e+00]
  Bounds range    [0e+00, 0e+00]
  RHS range       [2e-01, 4e+05]
Presolve time: 0.00s
Presolved: 13 rows, 85 columns, 305 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0   -1.0000000e+03   0.000000e+00   3.798884e+06      0s

Solved in 6 iterations and 0.00 seconds
Unbounded model


Any help is appreciated.

Many Thanks,

Angelos

[T.]

I checked your model with an exact solver and it is in fact infeasble. In addition to that, the dual is unbounded with a relatively sparse dual ray (= certificate of infeasibility).

If I do:

gurobi> m=read('withextra.lp')

gurobi> setParam('PreDual',0)

gurobi> setParam('DualReductions',0)

gurobi> m.optimize()

, then Gurobi says: "Solved in 0 iterations and 0.00 seconds" and "Infeasible model".

If I do:

gurobi> m=read('withextra.lp')

gurobi> setParam('PreDual',0)

gurobi> m.optimize()

, then Gurobi says: "Infeasible or unbounded model".

If I do:

gurobi> m=read('withextra.lp')

gurobi> setParam('PreDual',1)

gurobi> setParam('DualReductions',0)

gurobi> m.optimize()

, then Gurobi says: "Unbounded model".

Altogether, I think the following happens: With your settings, Gurobi takes the dual of the model. Gurobi then calls this the "model" and claims unboundedness. While this is correct, I think the output in such a case should be improved.

When you disable taking the dual, then I guess, Gurobi detects infeasibility of a reduced dual model and correctly claims "Infeasible or unbounded model". Disabling dual reductions yields the correct result "Infeasible model".

[Angelos Tsoukalas]

Thanks! I'll use the setting you suggested.

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[Renan Garcia]

Angelos,

Thank you for reporting this issue. The Gurobi developers have tracked down the corresponding bug, and the fix will appear in a subsequent release.

T.,

Thanks for providing a suitable workaround.

[Tung Vu Xuan]

Hi, 

I am using Gurobi 7.0.1. I have a model that has a constant objective (0) as in attached. Gurobi returns "unbounded" for this model which is not true in LP. If I do "setParam('PreDual',0)", Gurobi return feasible. Do you have any ideas for this? Thanks.

Vào 18:52:22 UTC+2 Thứ Năm, ngày 21 tháng 4 năm 2016, Renan Garcia đã viết:

[Renan Garcia]

If I run this model with Gurobi 7.0.1, I see the following in the logs:

  Warning: very big Kappa = 5.56043e+12, try parameter NumericFocus

This means the condition number for the optimal basis is very large, which causes issues for the solver.

<mip1.lp.gz>

[Renan Garcia]

Try setting the ScaleFlag parameter to 0 or 2 (see http://www.gurobi.com/documentation/7.0/refman/scaleflag.html#parameter:ScaleFlag).

[Tung Vu Xuan]

It works for me now. Thank you very much!!

Vào 15:08:40 UTC+1 Thứ Sáu, ngày 02 tháng 12 năm 2016, Renan Garcia đã viết: