How can I recover the vector?

I got some trouble when applying SDP. Provided a complex-value matrix W is given, and we know |w|^2 = w*w’ = trace(w’*w) = W. How can we get the vector w according to W?

Please help me.

It is not clear what your problem is. Does your problem involve reformulation into an SDP with accompanying rank one constraint, with the rank one constraint (which is non-convex) dropped, in order to result in a convex problem? If so, there is generally no guarantee that the rank one constraint will be satisfied at the optimal solution of the SDP.

Actually, by invoking SDP, I obtained the solution by dropping the rank one constraint, namely I have got the matrix W. But I still do not know how to recover the vector w based on the matrix W.

Please show us your mathematical problem formulation, your CVX code, and the results, so that we know what you’re talking about.

I think he wants to find a w such that


if it is available. I think the literature has examples of that. Did not Goemans and Williamson get several prices for doing this?

In any case this is not a cvx question.