2015/11/14 by Canyi Lu, Lu, Canyi, Huan Li +5
Engineering · #Advanced Adaptive Filtering Techniques #Advanced MIMO Systems Optimization #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1511.05133
openalex publication_date 2015/11/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective consists of a smooth part and a nonsmooth but simple part. We propose the Fast Proximal Augmented Lagragian Method (Fast PALM) which achieves the convergence rate O(1/K2), compared with O(1/K) by the traditional PALM. In order to further reduce the per-iteration complexity and handle the multi-blocks problem, we propose the Fast Proximal ADMM with Parallel Splitting (Fast PL-ADMM-PS) method. It also partially improves the rate related to the smooth part of the objective function. Experimental results on both synthesized and real world data demonstrate that our fast methods significantly improve the previous PALM and ADMM.