Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration

Clarice Poon, Jingwei Liang

Published 2019-06-24Version 1

The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity and efficiency. Over the years, different efforts are made to improve the method, such as the inertial technique. By studying the geometric properties of ADMM, we discuss the limitations of current inertial accelerated ADMM and then present and analyse an adaptive acceleration scheme for ADMM. Numerical experiments on problems arising from image processing, statistics and machine learning demonstrate the advantages of the proposed algorithm.