An Empirical Study of ADMM for Nonconvex Problems

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 `0 regularized linear regression, `0 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.