Supplement: Proximity Operator of the Matrix Perspective Function and its Applications Joong-Ho Won Department of Statistics Seoul National University wonj@stats.snu.ac.kr A Proofs A.1 A key lemma

Proofs of both Theorems 2 and 4 are based on the following key lemma, Lemma A.1. To prove this lemma, we begin by recalling the definition of directional derivatives. F (x + t h) F (x) t if the limit exists. Now we can prove the lemma: Proof of Lemma A.1. The following lemma shows a representation of an element of this set in terms of M: Lemma A.3.