I have the following problem to solve:
\quad\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}}
\quad\quad~0 \leq \beta_{i} \leq 1, ~~i = 1,2
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.