Check if Matrix is Unitary in CVX

Nonconvex
1

In the “subject to” conditions, is it possible to check if some variable defined between the cvx_begin and cvx_end tags is unitary?

cvx_begin sdp
variable X(n,n);
subject to
    % Check if X is unitary.
cvx_end

A matrix is unitary if U U^* = U^*U = I or equivalently if U^{-1} = U^*

However doing either check as

cvx_begin sdp
variable X(n,n);
subject to
    X * X' == eye(n,n); % CVX complains about invalid quadratic form.
    inv(X) == X'; % CVX doesn't know what "inv" is.
cvx_end

Even attempting to go through with individual for loops and multiply scalar by scalar to yield a new matrix does not agree with CVx. Any feedback would certainly be greatly appreciated.

2

You cannot do this. It is not convex.