Fast Proximal Linearized Alternating Direction Method of Multiplier with Parallel Splitting

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.

Authors

• Canyi Lu
• Huan Li The State Key Laboratory of Blockchain and Data Security, Zhejiang University Hangzhou High-Tech Zone (Binjiang) Institute of Blockchain and Data Security
• Zhouchen Lin National Key Lab of General AI, School of Intelligence Science and Technology, Peking University Peng Cheng Laboratory
• Shuicheng Yan Skywork AI, Singapore Nanyang Technological University, Singapore

Keywords

No keywords are indexed for this paper.