Direct input of PSD constraints

[cgois]

Although a variable can be declared to belong in the PSD cone (e.g., foo = @variable(problem, [1:dim, 1:dim] in COI.HermitianPSDCone())), I have not yet found a way to directly input PSD constraints.

For example, I frequently would like to impose things of the sort @constraint(problem, operation(foo) in COI.HermitianPSDCone()), where operation is any transformation on the variable.

My current workaround is to introduce a new variable in the PSD cone and enforce equality constraints, for instance:

"""
Enforce PSD constraint on the input matrix.
Uses dummy vars. to enforce PSD (not possible directly in ComplexOptInterface?).
"""
function ispsd(problem::Model, A::AbstractMatrix)
    @assert size(A,1) == size(A,2) "Matrix must be square."
    @assert length(size(A)) == 2 "Matrix must be bidimensional."

    dim = size(A, 1)
    PSD = @variable(problem, [1:dim, 1:dim] in ComplexOptInterface.HermitianPSDCone())
    @constraint(problem, A .== PSD)
end

then call ispsd(problem, operation(foo)).

Is there a more economic way to do this? Or maybe does ComplexOptInterface already support PSD constraints directly?

[blegat]

This is not possible yet but I'm going to add this feature when we merge this package into JuMP as part of https://jump.dev/announcements/2022/04/19/small-development-grant/