Y_k = Z_k \, Z_k^\intercal

This line gives the error. Where Z_k is a CVX mixed positive constant/real affine expression (7\times 1) vector.

Y_k = Z_k \, Z_k^\intercal

This line gives the error. Where Z_k is a CVX mixed positive constant/real affine expression (7\times 1) vector.

This is non-convex. But you haven;t shown us how this will be used/ So perhaps it can be reformulated? Do you perhaps want the semidefinite relaxation of this?

(17a) to (17g) appears to be a Linear Programming problem, requiring only the declaration of `Y`

as a CVX variable, and not involving Z_k at all.

My goal is the find \mathbf{w}_{k,i}. Is it possible to initialise the variables in \mathbf{w}_{k,i} randomly (with proper boundary conditions), and then declare Y as CVX variable inside begin/end CVX?

I have no idea what this optimization model represents or any understanding of its input data. From CVX’s viewpoint, you can create input data any way you want, provided that the resulting CVX problem follows CVX’s rules. It’s up to you whether that is a meaningful problem to solve.

Looking more carefully at (17a) to (17g), the objective is written in terms of a single Y_{ki}, but `i`

apparently goes from 1 to N. So if N \ne 1, the objective function doesn’t even appear to be well defined.