Need help with formularizing a problem with matrix quadratic form

Hi all,
I have an optimization problem as following.

variable w(P,1)
minimize ||K-(w*w')*K*(w*w')||
subject to norm(w)=1

where the matrix K is a given P-by-P symmetric PSD matrix.

I have read a few tutorials about SDP problems but I haven’t got an idea how could I formulate my problem as an SDP problem.
Thanks for any advice in advance!

CVX cannot solve this problem.