3D variable in JuMP

Specific Domains Optimization (Mathematical)
1

I am working on a convex optimization problem that needs to define several (e.g. 5) symmetric matrices as variables. I was wondering if it is possible to define those variables with a single line like @variable(m, x(N,N,M), Symmetric), where N is the dimension of the matrix, and M is the number of copies of symmetric matrices. Then I can access a symmetric matrix by, e.g., x[:,:,1].

From this post (Semidefinite relaxations of quadratic constraint - CVX Forum: a community-driven support forum), it seems to be possible in CVX. So I was thinking it would be nice if I could do similar things in JuMP.

2

This is not yet possible in JuMP, you need to do

x = Array{JuMP.VariableRef}(undef, N, N, M)
for i in 1:M
    x[:, :, i] = @variable(m, [1:N, 1:N], Symmetric)
end

or do

x = [@variable(m, [1:N, 1:N], Symmetric) for i in 1:M]
3

Thank you for the promp reply!

The second code works for me. I also have two tips for implementing this as a future reference:

  1. In order to make the model more readable, I set the names of the matrices as follows: x = [@variable(m, [1:N, 1:N], base_name = "x$i", Symmetric) for i in 1:M]. Then in the printed model an item in the first matrix looks like this: x1[i,j].

  2. To access the ith matrix, use x[i][:,:]

For the first option though, I get a bug from x = Matrix{JuMP.VariableRef}(undef, 2, 2, 3), which says MethodError: no method matching Array{VariableRef,2}(::UndefInitializer, ::Int64, ::Int64, ::Int64). I assume this is because JuMP does not support 3-dimensional variables.

4

Oops, Matrix should be replaced by Array in the first code.

5

Now it works. In this case the ith matrix is accessed by x[:,:,i].