$$ \max\limits_{\mathbf{f},\ \|\mathbf f\|=1 } \log_2\left(\prod^K_{i=1} \ \frac{ \mathbf{f}^H {\mathbf E} (\mathbf{W}_i, \Theta, \tau_i) \mathbf{f}} { \mathbf{f}^H \mathbf{G}_i ( \mathbf{W}_i, \Theta, \tau_i) \mathbf{f} } \right) $$
For the product of Rayleigh quotients in the above problem, solution $\psi_i\in (M\times1)$, corresponding to the largest eigenvalue $\zeta_i$, for the $N \times N$ matrix pairs $E$ and $G_i$ is obtained. So, for $K$ product terms, $K$ solutions instead of one is obtained.
How to find an unique solution for this problem?