NIPS 2017
Mon Dec 4th through Sat the 9th, 2017 at Long Beach Convention Center
Paper ID: 947 A New Alternating Direction Method for Linear Programming

### Reviewer 1

The paper is well written and discusses an interesting problem of linear program method which is applicable to several optimization procedures. It is not completely clear on which data set (experimental setup) FADMM algorithm is evaluated, I would expect at least a small paragraph on this, or providing references to the existing setups.

### Reviewer 2

This paper presents a new splitting method approach to the linear programming problem which has theoretical and practical performance advantages over existing approaches. Experiments are given showing the performance gains on a variety of problems that arise from reformulations of machine learning problems. I like the approach taken by this paper. First order approaches to the LP problem are under-studied in my opinion. The most notable papers are from the early 90s. The recent resurgence in the popularity of ADMM style splitting methods in the NIPS community makes this paper relevant and timely. In particular, the method given relies on recent advances in solving well-conditioned unconstrained least-squares problems which were not known the in 90s. The presentation of the paper is generally good. The graphs and tables are legible and explained well. The experiments are more comprehensive than typical NIPS papers. Often papers on the LP problem report results on the old NETLIB suite. They are very different in structure from the ML problems considered in this work, so it's not obvious that the same approaches should work well on both. I think it's fine for the NIPS paper to consider just ML problems; It would be interesting to see results on the NETLIB problems though. There are some minor grammatical issues in the text. I've pointed out a few below. Otherwise well written. “compared with current fastest LP solvers” “linearly at a faster rate compared with the method in [9]” “The work [10] prove that” line 100. “equivalent to solve a” line 123. “Let the gradient (8) vanishes” line 201.