How to create a variable that is Hermitian but not PSD?

Specific Domains Optimization (Mathematical)
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1

I need to create a Hermitian matrix that is not PSD for solving a specific problem. How do I do that? The obvious syntax @variable(model, x[1:d,1:d], Hermitian) gives an error, unlike @variable(model, x[1:d,1:d], Symmetric).

I suppose I could do @variable(model, x[1:d,1:d] in ComplexPlane()) followed by @constraint(model, x .== x') but that’s terribly inefficient.

2

There is no syntax support for this yet. Open a feature request in the JuMP repo.