My problem is a quadratically constrained quadratic program (QCQP) and can be find as follows:
min V’ * P * V
s.t. sum( V’ * A_i * V ) >=0, i=1,…,m (1)
sum( V’ * B_j * V ) <=0, j = 1,…n
Trace( V * V’ ) >0
where P,A_i,B_j are positive semidefinite. V is a N * 1 vector.
My question is that I can use SDP method to solve this problem and get Q=V * V’, and then decompose Q to get x in order to get the mmse receiving beamformer Ummse. However, the problem is that Q are often full rank according to my simulation results via with the aid of cvx tools. This will conflict with Rank(Q)=1.
If there is no (1), I can solve this QCQP via cvx instead of SDP method . However, since the first constraint is a convex >=0, perhaps the problem above is nonconvex one. How to relax it or deal with it in that case?
I will be appreciated if anyone can transform it to a convex problem which can be solved via the aid of cvx tools.
Look forward to your reply!
Edit by MLS: Corrected typo in thread title from “concave” to “convex”.