Minimizing the norm of an expression containing a hermitian matrix to some power

1

Hello all.

I am a newbie at cvx and after reading through the guide I am still stumped. I have the following problem

variable H(n,n) hermitian semidefinite
minimize norm (diag([v])- BHH’*B)

where v is a vector of n numbers and B is an n\times n matrix. I keep getting a Disciplined convex programming error telling me that only scalar quadratic forms are allowed. As this is only one of the two terms of the real objective function i want to minimize (the other involves terms that are linear in H), i have tried several other small tricks (like declaring H^2 as my variable and using sqrtm(H) in the second term) but to no avail.

Can somebody help with how to properly define an objective function that uses a semidefinite Hermitian matrix and its complex conjugate?

Regards

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Is this convex? If not, CVX is not your tool.
If so, how would you go about proving it? The proof will likely lead to the proper way to express it in CVX.