The solution of Semidefinite Programming (SDP) violates the constraints

Specific Domains Optimization (Mathematical)
2

Here is what I get

julia> value.(x)*u'-value.(X)
3×3 Matrix{Float64}:
  4.63377e-10  -2.53719e-10  1.44575e-9
  3.61053e-10  -2.6613e-10   2.56338e-9
 -3.33895e-10   1.68968e-10  1.42857e-11

julia> eigvals([1 value.(x)'; value.(x) value.(X)])
4-element Vector{Float64}:
 -3.4264861390395915e-10
 -7.479956860042055e-11
  1.7273934867396232e-9
  3.999999996555678

The biggest violation for the first constraint is -2.53719e-10 and the biggest for the second is -3.4264861390395915e-10 which is within the tolerance so I don’t think there is any issue.

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