A Remaining Proofs from Section 4

Here we provide proofs for all the results in Section 4 that were excluded in the main paper. Here we prove important properties of our convex program. We start by recalling properties showed in [CSS19a]. Function f (X) is convex in X. Theorem A.2 The function f (X) is separable in each row and we define following notation to capture it. The above derivation satisfies the conditions of the lemma and we conclude the proof.