  The alternating direction method of multipliers (ADMM) is a common
optimization tool for solving constrained and non-differentiable problems. We
provide an empirical study of the practical performance of ADMM on several
nonconvex applications, including l0 regularized linear regression, l0
regularized image denoising, phase retrieval, and eigenvector computation. Our
experiments suggest that ADMM performs well on a broad class of non-convex
problems. Moreover, recently proposed adaptive ADMM methods, which
automatically tune penalty parameters as the method runs, can improve algorithm
efficiency and solution quality compared to ADMM with a non-tuned penalty.
