Nonconvex constraint

Hello everyone

I have problem with following non-convex constraint :


Definition of vec() function:
“the vectorization of an m×n matrix A, denoted by vec(A), is the mn × 1 column vector obtained by stacking the columns of the matrix A on top of one another”

y,A and S are known and B is one of my optimzation problem variables.

size(B)=[Q,M],size(S)=[M M] and S is diagonal.
when i use cvx following error happens:

Error using  *  (line 126)
 Disciplined convex programming error:
    Only scalar quadratic forms can be specified in CVX .

 Error in DOA_Sparsity (line 65) 
   norm((y-(A * vec(B*S*B'))),2) <= eta;

It is clear that vec(B*S*B') makes the constraint non-convex,anybody have idea for change this expression to convex? I tried to change it using relaxation techniques,but my effort failed.

Thanks for your Help.

FAQ: Why doesn’t CVX accept my problem? [READ THIS FIRST]