YALMIP
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Complex-valued dualize fails with complex-valued equalities
X = sdpvar(3,3,'hermitian','complex')
e = X(1,2)-(2 + sqrt(-1)*3);
Model = [[eye(3) zeros(3);zeros(3) X] >= 0, e == 0];
optimize(Model,trace(X),sdpsettings('dualize',1))