Improves infeasibility ray check of lineartest8

[blegat]

The dual of the constraint does not have to be -1, it can be scaled by any positive constant since it is a ray.

[joaquimg]

Actually I cant approve :( Xpress does not return rays for variable bounds.
However I need the first part because the constraint ray should be just negative as you fixed

[mlubin]

Xpress does not return rays for variable bounds.

Are you sure? That seems strange.

[joaquimg]

Yep, pretty sure. At least for Xpress up to 8.0 version (the last is 8.3).

They have a get[primal/dual]ray API that is a bit limited.

[blegat]

Can't you determine the value of the ray for the variable bounds using the model and the value of the ray for the constraints ?

[joaquimg]

How?

[blegat]

In the test of this PR for example, the problem is

min x
s.t. 2x+y <= -1
x,y >= 0

so the dual is

max -z
s.t.
1 - 2z >= 0 dual of x >= 0
-z >= 0 dual of y >= 0
z <= 0 dual variable of constraint

when you look for a ray, it becomes

max -z
s.t.
-2z >= 0
-z >= 0
z <= 0

The value of the variable bounds are the slack of the first and second constraint of the dual hence the checks yd ≈ -cd and xd ≈ -2cd of this PR (z is cd).

[joaquimg]

Oh, I see, you mean having the interface to compute these

[blegat]

@joaquimg Is Xpress ready to pass the test with the changes of this PR now ?

[joaquimg]

Nope. It does not returns an infeasibility certificate with the bounds. I also think Gurobi and CPLEX won’t do it.

[mlubin]

Ok to close now given #159?

[blegat]

I still think this test should be finished.

[blegat]

@joaquimg I just checked, Gurobi passes linear12 test and linear8 test with the modification of this PR.

[joaquimg]

That is interesting, I am pretty sure I do not set Gurobi's "FarkasDual" for bounds. Are we just having some luck?

[blegat]

What do you return as dual of the variable bounds ?

[joaquimg]

I should be writing NaN. My Gurobi licence expired, I will update it tomorrow.

[blegat]

Replaced by JuliaOpt/MathOptInterfaceTests.jl#34