Trace minimization in CVX

I have the following problem:
C(n,m) and D(n,m) are two given matrices and I have two unknown dependent variables T(n,n) and B(n,m) where B=D+T*C.
I need to find B that minimizes trace[B’*B + inv(B’*B)] with constraint in the L_2 norm of T , i.e. norm(T,2)<=0.05. Then from B I can find T.

it turned out that the inv operator in cvx environment is undefined
and even if I use trace_inv operator it still doesn’t work.

Can anybody tell me what’s wrong in this code.

Yes, CVX will not accept the B'*B construct. That is a basic violation of the disciplined convex programming ruleset.

Now, trace(B'*B) is actually just sum_square(vec(B)), so that term can be handled relatively easily. But I do not know how to express trace_inv(B'*B) in a compliant manner.

yes I have already solved the first part using the sum of the scalar quad_form but still looking how I can write the inverse similarly…

I’m afraid I do not know if an equivalent DCP-compliant form exists.