Access to dual value of constraints of the master problem

[diHnguyen]

Hello,

I would like to access the duals associated with the constraints in the master problem for a separate model, and it seems like I can't if they are added as lazy constraints. (I could be completely wrong about this, but I did not see a solution when looking into the topic.)

Would it be possible to iteratively add constraints to the master problem without the use of lazy constraints, perhaps something similar to @constraint() in JuMP?

Thank you so much!

[guimarqu]

Hello,

The only way to generate constraints during optimization is to use the method MOI.submit in a pricing callback (non-lazy or user cuts).
At the moment, it's indeed not possible to retrieve the dual of the constraint added during the optimisation.
However, last month, we implemented a feature (#547) which will allow us to implement this very easily.

As I'm going to be busy the next 2/3 weeks, I don't think I'll have time to implement that and write the tests.
If you need this feature very quickly, I would be very grateful if you could share a very little example with some expected dual values of the constraints. I'll put this example in the unit tests and I'll make it work in the master branch.

Thanks for the report !

[diHnguyen]

Hi @guimarqu ! Thank you for the quick response. Here is a tiny example of what I can see

#Variables
@variable(model, 0<= x[1:7] <= 1)
@variable(model, y[1:2] >= 0)
@variable(model, u >=0)

#Constraints
xCon = @constraint(model, sum(x[i] for i = 1:7) <= 1)
yCon = @constraint(model, sum(y[i] for i = 1:2) == 1)
initCon1 = @constraint(model, u >= 0.9*y[1] + y[2] - x[1] - x[2] - x[3])
initCon2 = @constraint(model u >= y[1] + y[2] - x[7])

#Objective function
@objective(model, Min, u)

Solving model with no additional constraint added:

#Solutions
u = 0.45
x = [0.45,0,0,0,0,0,0.55]
y = [1,0]

#Corresponding dual solutions to the following constraints
xCon : -0.5
yCon : 0.95
initCon1 : 0.5
initCon2 : 0.5

Some additional results in case they can be useful. If we solve model with an additional constraint, newCon, added:

newCon = @constraint(model, u >= y[1] + 0.9*y[2] - x[5] - x[6])

then the solution is:

#Solutions
u = 0.6333
x = [0.3667,0,0,0,0.2667,0,0.3667]
y = [0,1]

#Corresponding dual solutions to the following constraints
xCon : -0.333
yCon : 0.9667
initCon1 : 0.333
initCon2 : 0.333
newCon: 0.333

Thanks again for your help!

[guimarqu]

Hi,

thanks for the MWE,

In the tests, you have an example of how you can retrieve the dual value of the cut :

The callback

Coluna.jl/test/issues_tests.jl

Lines 432 to 443 in d79d546

	callback_called = false
	constrid = nothing
	function my_callback_function(cbdata)
	if !callback_called
	con = @build_constraint(u >= y[1] + 0.9*y[2] - x[5] - x[6])
	constrid = MOI.submit(model, MOI.LazyConstraint(cbdata), con)
	callback_called = true
	end
	return
	end
	MOI.set(model, MOI.LazyConstraintCallback(), my_callback_function)

The line to get the dual value

Coluna.jl/test/issues_tests.jl

Line 450 in d79d546

@test MOI.get(JuMP.unsafe_backend(model), MOI.ConstraintDual(), constrid) ≈ 0.33333333

It will be available in the next release (very soon).

[diHnguyen]

This is wonderful! Thank you!!