I have a function in the variables $x_{kl};\ k,l=1\ldots,m$,
$$\sum_{i=1}^n \sum_{j=1,j<j'}^{N_i}\left( b_{ij} b_{ij'}- \sum_{k,l=1}^{m}x_{kl}f_k(a_{ij})f_l(a_{ij'})\right)^2$$
where $a_{ij},b_{ij}$ are known constants and $f_k$ are known functions. Moreover, we must let $x_{kl}=x_{lk}$. How can I solve this using CVX, or is there an (easy for those who have experience, because this looks a little bit like the least squares estimator) expression for the solution? Can I use CVX if the unkown is a matrix?