This paper provides an AMP-based algorithm to solving SLOPE, a variant of the regularized least squares problems with a non-separable regularizer, and a proof that state evolution describes the macroscopic behavior of the proposed algorithm under the iid zero-mean Gaussian design and in the large-system limit. All the three reviewers rated this paper above the acceptance threshold. They are also satisfied with the authors’ feedback. I would thus recommend acceptance of this paper for presentation at the NeurIPS conference. Reference 20 has been published in the proceedings of the IEEE International Symposium on Information Theory, so that I would suggest updating the entry to reflect it.