  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, flexibility and efficiency. Over the years, numerous efforts are
made to improve the performance of 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 analyze an adaptive
acceleration scheme for the method. Numerical experiments on problems arising
from image processing, statistics and machine learning demonstrate the
advantages of the proposed acceleration approach.
