The objective is as follows:
$\min_{\mathbf{F}} a Tr(\mathbf{F} \mathbf{F}^H) - \mathbf{b}\mathbf{F}^H \mathbf{C} \mathbf{F} \mathbf{d}$
$s.t.\ \ \ Tr(\mathbf{F} \mathbf{F}^H)<p$
where $a$ and $p$ are scalars, $\mathbf{b}$ is $1 \times N$ real vector, $\mathbf{d}$ is $N\times 1$ real vector, $\mathbf{C}$ is $N \times N$ Hermitian transpose matrix, $\mathbf{F}$ is $N \times N$.
It is obvious that if all the variables are scalars, the optimal $F^\ast$ is either $0$ or $p$. So how about the matrix case?
Thanks!