We thank Reviewers (R) 1, 2, 3, and 4 (who gave us marks 7, 6, 8, 6 respectively) for their positive feedback on the

Just as proximal methods in Euclidean optimization, the FB scheme relies on subroutines to compute the JKO step. G], and discuss more precisely our numerical results. These splitting methods are indeed related, we will cite the missing references [[1,2,3,6]]. Also, it is not covered in [[1,2,3,6]]. This is an interesting question.