I have the following problem to solve:
\mathop{\mathrm{min}}\limits_{\mathbf{f},{\beta}_{i},i=1,2}\quad\mathbf{f}^{H}\mathbf{Q}_{0}\mathbf{f}\\
\text{s.t.} \quad\mathbf{f}^{H}\mathbf{Q}_{1}\mathbf{f}\geq\frac{\sigma_{n}^{2}}{\beta_{1}}\\
\quad\quad\mathbf{f}^{H}\mathbf{Q}_{2}\mathbf{f}\geq\frac{\sigma_{n}^{2}}{\beta_{2}}\\
\quad\quad\mathbf{f}^{H}\mathbf{Q}_{3}\mathbf{f}\geq\frac{\varepsilon_{1}}{1-\beta_{1}}\\
\quad\quad\mathbf{f}^{H}\mathbf{Q}_{4}\mathbf{f}\geq\frac{\varepsilon_{2}}{1-\beta_{2}}\\
where \mathbf{f}\in \mathbf{C}^{N\times 1},\mathbf{Q}\in \mathbf{C}^{N\times N}.
This problem is a SDP? Why can not I obtain the optimal solution by the CVX? Does any one have experience with this? Thanks.