Relaxation of variable times variable

Hi all,

I am new to cvx and convex optimization.

I want to implement a SDP model where one of the constraints is on the form of

X == a*a’ (where X and a are variables). I know this is not allowed as per the DCP rules.

My question is, what are ways to overcome (relax) this constraint? Is there a general approach? I appreciate a guidance in where and what I should be looking for. Many thanks in advance.

There is convex relaxation to X \succeq a*a' implemented by Schur complement by declaring X symmetric and writing
[X a;a' 1] >= 0
if CVX is in SDP mode.