SOS use on multidimensional arrays

Specific Domains Optimization (Mathematical)
1

Hello all!
I am trying to use the new way of SOS2 constraints (MOI.SOS2) but since I have a 3-dimensional variable (the last dimension should be part of the SOS2 set), existing examples are not sufficient. Any hints how to expand? Using the following code does not work

P = 10
Q = 5
@variable(m,0<=test[1:P,1:Q]<=1)
for p = 1:P
@constraint(m, test[p] in MOI.SOS2(collect(1:Q)))
end

and results in the error: ERROR: In @constraint(m, test[p] in MOI.SOS2(collect(1:Q))): unable to add the constraint because we don’t recognize test[1,1] as a valid JuMP function.

I would have expected that since in the example x[1:3] is referred to as x in the SOS2-constraint this would have been sufficient. I would not like to step into more inconvenient modeling approaches but think this should be straightforward and supported by MOI!

Thankful for all solutions!

2

This question needs more context, please provide a complete example.

In the meantime, you could try test[p, :] in ....

3

In your code, test is an Array{VariableRef, 2}. But test[p] just selects one element, not a vector. This isn’t specific to JuMP. See:

julia> x = rand(3, 3)
3×3 Array{Float64,2}:
 0.0576085  0.285097  0.125166
 0.701127   0.35993   0.462062
 0.727124   0.182186  0.378751

julia> x[1]
0.05760854662389847

As @leethargo says, you need a slice: test[p, :] :slight_smile:

p.s. You might want to read Please read: make it easier to help you. It has some advice of formatting the code in questions and making a minimum working example.

4

Thank you!

Unfortunately using test[p,:] results in …

Constraints of type MathOptInterface.VectorOfVariables-in-MathOptInterface.SOS2{Int64} are not supported by the solver and there are no bridges that can reformulate it into supported constraints.

Here the entire “dummy” problem…

model = Model(with_optimizer(Gurobi.Optimizer, env, OutputFlag=1))
P = 10
Q = 5
@variable(model,0<=test[1:P,1:Q]<=1)
for p = 1:P
@constraint(model, test[p,:] in MOI.SOS2(collect(1:Q)))
end
@objective(model, Max, sum(i*test[i,j] for i=1:P, j=1:Q))
optimize!(model)

My real problem is a very large MILP where I try to represent a working point of a unit i at each time t with a piecewise linear function using some lambda-variables, i.e.
level[i,t] = sum(lambda[i,t,p]*coeff[p] for p=1:pc)
This is needed to handle some nonlinearities and is possible to do via GAMS/AMPL but I would like to be able to formulate these more complex PWL in Julia.

5

This bug will be fixed in the next release of JuMP. For now, you need

@constraint(model, test[p,:] in MOI.SOS2(collect(1.0:Q)))
                                                  ^^ Note this
6

Great, now working! Thank you!!!