Are you sure it won’t work the simple way? It seems to for me:
julia> f(i) = 2i -1
f (generic function with 1 method)
julia> using JuMP
julia> m = Model()
Feasibility problem with:
* 0 linear constraints
* 0 variables
Solver is default solver
julia> @variable(m, y[i = 1:3, j = 1:f(i)] >= 0, start = i + j)
y[i,j] >= 0 for all i in {1,2,3}, j in {..}
julia> getvalue(y)
y: 2 dimensions, 9 entries:
[1,1] = 2.0
[2,1] = 3.0
[2,2] = 4.0
[2,3] = 5.0
[3,1] = 4.0
[3,2] = 5.0
[3,3] = 6.0
[3,4] = 7.0
[3,5] = 8.0
Do you get an error if you try that?