Update SDP Formulations to use SkewSymMatrixSpace

[kibaekkim]

I wonder if this variable WI should have been created as Symmetric.

PowerModels.jl/src/form/wrm.jl

Lines 52 to 53 in 12d560e

	WI = var(pm, nw)[:WI] = JuMP.@variable(pm.model,
	[1:length(bus_ids), 1:length(bus_ids)], base_name="$(nw)_WI", start=0.0

[ccoffrin]

This is a good question! In fact the matrix is SkewSymmetric, not strictly Symmetric. SkewSymmetric was not supported in JuMP when we first implemented this, but if it is now available this constraint can be updated.

[kibaekkim]

Great. I see the relevant PR: jump-dev/JuMP.jl#2147 Looking forward to that!
I will just leave this open until resolved, but please feel free to close, if you want.

[ccoffrin]

I looked unto this and the following point needs to be resolved before this can be addressed. jump-dev/JuMP.jl#2884

[odow]

See also #345 (comment)

We can now do

julia> model = Model();

julia> @variable(model, x[1:2, 1:2] in HermitianPSDCone())
2×2 LinearAlgebra.Hermitian{GenericAffExpr{ComplexF64, VariableRef}, Matrix{GenericAffExpr{ComplexF64, VariableRef}}}:
 real(x[1,1])                    real(x[1,2]) + imag(x[1,2]) im
 real(x[1,2]) - imag(x[1,2]) im  real(x[2,2])

julia> real.(x)
2×2 Matrix{AffExpr}:
 real(x[1,1])  real(x[1,2])
 real(x[1,2])  real(x[2,2])

julia> imag.(x)
2×2 Matrix{AffExpr}:
 0              imag(x[1,2])
 -imag(x[1,2])  0