what is the advantage of using `[I x;xT z]>0`

constraint rather than `norm(x).^2<z`

constraint in cvx? In my problem the objective function is not linear and so I cannot use SDP.

I am afraid I donâ€™t understand what you are asking. I would certainly NOT use the SDP form, but rather `sum_square(x) ``<``= z`

. CVX 3.0 can handle `norm(x).^2 <= z`

natively as well.