Reference required for Alternating Direction Method for Multipliers?

Question

In my understanding, Alternating Direction Method for Multipliers (ADMM) is widely viewed as a tool to parallelize large-scale convex-optimization problems arising in statistics and other related fields.

The following paper by S. Boyd is a good reference https://web.stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf

But one can also use, like Help needed to define a constraint in an optimization problem?, ADMM to solve non-convex problems

I am looking for a paper that I can cite when ADMM is used for solving otherwise non-convex problems?

Answer 1

First of all, ADMM stands for Alternating Direction Method of Multipliers.

ADMM for nonconvex functions is a current hot research topic.

I recommend the following theoretical papers:

1. Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems by Hong et al.
2. Global Convergence of ADMM in Nonconvex Nonsmooth Optimization by Wang et al.

Applications: see the references cited in the above papers (read, for example, the third paragraph on page 2 of the second paper).

Answer 2

ADMM has been around since the 70's (e.g Glowinski's works). For references, look at the first part of my answer to a similar question here. Hope this helps.