Could you please provide some hints for me to solve this optimization problem?
Here, for any $i=1,2$ and $j=1,2$, $\phi_i$ and $\psi_j$ are unknown vectors, $\alpha_i$, $\beta_j$ are some known vectors, $A_{ij}$ is matrix. The optimization problem is
$\max_{\phi_i,\psi_j} \sum_{i=1}^2 \sum_{j=1}^2 (\phi_i' A_{ij} \psi_j)^2$
$s.t. \phi_i'\phi_i = \psi_j'\psi_j=1$, for any $i=1,2$, $j=1,2$ and $\phi_i'\alpha_i = \psi_j'\beta_j=0$, for any $i=1,2$, $j=1,2$