Add comprehensive tests for Farkas certificates

[odow]

Implemented in solvers:

• Add Farkas duals for variable bounds Clp.jl#105
• Add farkas certificate for variable bounds CPLEX.jl#337
• Add infeasibility certificate for variable bounds GLPK.jl#155
• Add farkas dual for variable bounds Gurobi.jl#363

Solvers like Xpress probably still need to be updated.

[blegat]

Does this closes #433 ?

[odow]

I think it resolves the general issue and adds tests. I'm pretty happy with the convention of removing objective constants.

I don't understand the question about constants in ConstraintPrimal or ObjectiveValue.

[blegat]

This is for unbounded rays, in that case, the equivalent of "removing objective coefficients" is "remove constraints constants".

[odow]

Does it make sense to query ConstraintPrimal and ObjectiveValue for a ray though? Isn't it really just VariablePrimal?

[blegat]

Can't you query DualObjectiveValue for infeasibility ray ? I need it to create infeasibility cut in SDDP. There is a get_fallback for ObjectiveValue and ConstraintPrimal if the solver does not provide that.

[odow]

Ah. DualObjectiveValue is a reasonable thing to query. I guess the decision is whether to query the "beta" term here, or whether to query the complete RHS.

[blegat]

If you have the problem
c1: x + y = 1
c2: x >= 1
c3: y >= 1
The dual is
max y1 + y2 + y3
y1 + y2 == 0
y1 + y3 == 0
y2, y3 >= 0
You are wondering whether we should include y2 + y3 in the objective ?
An infeasibility ray is y = (-1, 1, 1). If we only include y1, we have -1 and with the full objective, we have 1. The correct answer is 1 IMO

[odow]

Yes, the DualObjectiveValue should be 1.

Let's merge this for now. It adds tests that the solvers already support. I'll need to go through and fix DualObjectiveValue in the solvers before we can add tests in MOI, so that can be done in a separate PR.