An Empirical Study of ADMM for Nonconvex Problems
This is an incremental empirical analysis for optimization researchers, showing ADMM's applicability to nonconvex domains.
The study tackled the practical performance of ADMM on nonconvex problems like l0 regularized linear regression and phase retrieval, finding that ADMM performs well and adaptive methods improve efficiency and solution quality compared to non-tuned versions.
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.