Multiblock ADMM with nesterov acceleration

Abstract

ADMM (alternating direction methods of multipliers) is used for solving many optimization problems. This method is particularly important in machine learning, statistics, image, and signal processing. The goal of this research is to develop an improved version of ADMM with better performance. For this purpose, we use combination of two approaches, namely, decomposition of original optimization problem into N subproblems and calculating Nesterov acceleration step on each iteration. We implement proposed algorithm using Python programming language and apply it for solving basis pursuit problem with randomly generated distributed data. We compare efficiency of ADMM with Nesterov acceleration and existing multiblock ADMM and classic two-block ADMM.