No. The key is to look at what is actually created:
julia> using JuMP
julia> N = 10
10
julia> S = [(1, 1, 1), (N, N, N)]
2element Vector{Tuple{Int64, Int64, Int64}}:
(1, 1, 1)
(10, 10, 10)
julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
julia> @variable(model, x1[i=1:N, j=1:N, k=1:N; (i, j, k) in S])
JuMP.Containers.SparseAxisArray{VariableRef, 3, Tuple{Int64, Int64, Int64}} with 2 entries:
[1, 1, 1 ] = x1[1,1,1]
[10, 10, 10] = x1[10,10,10]
julia> @variable(model, x2[S])
1dimensional DenseAxisArray{VariableRef,1,...} with index sets:
Dimension 1, [(1, 1, 1), (10, 10, 10)]
And data, a 2element Vector{VariableRef}:
x2[(1, 1, 1)]
x2[(10, 10, 10)]

x1
is a JuMP.Containers.SparseAxisArray
, with three dimensions and two nonzero keys.

x2
is a JuMP.Containers.DenseAxisArray
, with one dimension containing S
.
So you canâ€™t even index into x2
with three arguments:
julia> x2[1, 1, 1]
ERROR: KeyError: key 1 not found
What you could do is something like this:
julia> x2[[s for s in S if s[1] == 1]]
1dimensional DenseAxisArray{VariableRef,1,...} with index sets:
Dimension 1, [(1, 1, 1)]
And data, a 1element Vector{VariableRef}:
x2[(1, 1, 1)]