I found this optimization problem in the paper Signal Processing on Graphs: Causal Modeling of Unstructured Data equation 9:
where the last term is to ensure that $R_i $ commutes with other $R_j, j \ne i$ such that $[R_i, R_j] = R_iR_j - R_jR_i = 0. $ They say that this is an $\ell_1$ regularization problem. What I struggle with is how to combine the first and last terms into a single least square term. Ideally (which may no be possible) I am looking to have it in a canonical form of $\ell_1$ regularization, where I can plug it into one of the available $\ell_1$ regularization APIs.