I will assume each of \mathcal{F}_{x}, \mathcal{F}_{y}, \mathcal{F}_{z} are 2D (not 3D) symmetric positive semidefinite. Non-symmetry can be dealt with, but if not psd, your problem is non-convex.

You seen to want to solve some problem different than this, which would have a vector, not scalar, as argument of the norm. If so, you need to explain what the mathematical operation is between the vector and the 3D tensor which produces a vector. Show us a small example in MATLAB, not CVX, with numerical values for `psi`

in which you calculate the numerical value of the desired objective function.

```
cvx_begin
variables psi(N)
minimize(square_pos(psi * F_x * psi + square_pos(psi' * F_y * psi + square_pos(psi' * F_z * psi))
% Insert constraints. If there are no constraints, optimal variable values are all zeros.
cvx_end
```

If you really do have a quadratic form with 2D slices of a 3D tensor, then you ought to be able to apply `sum_suare_pos`

on the resulting vector to get the two-norm squared