I would like to know if there is a way to define a semi-orthogonal matrix in cvx.

U \in\mathcal{M}_{n,m} is a semi-orthogonal matrix if it’s a non-square matrix that satisfies U^T U=I and the columns of U are orthonormal for n>m (respectively the rows of U are orthonormal for n<m).

You cannot. This is not a convex set.

Yes you’re right!

Thanks.