Reviews: A primal-dual method for conic constrained distributed optimization problems

The reviewer believes that the greatest contribution of this paper is the analysis done for the time varying case, where the authors transformed the problem into one that requires a projection step into the consensual set; which then allows for applying a multi-consensus steps, where an inexact update analysis for primal-dual algorithms (Thm. This results leads to a converging distributed PDA algorithm for time varying networks. That said, the reviewer has several concerns on the practicality of the results and the presentation of this paper. To get around with the issue of computing (16)/(17) over time varying networks, the authors have adopted a multi-consensus step method to in (18) such that q_k k {p/2} consensus steps are needed for each iteration k, i.e., the number of steps grows with iteration number. The reviewer wonders if it is a practical setup as this essentially requires the algorithm to be synchronous, i.e., every node starts iteration k at the same time and knowing that he/she has to do exactly q_k times of consensus.