  The alternating direction method of multipliers (ADMM) is a versatile tool
for solving a wide range of constrained optimization problems, with
differentiable or non-differentiable objective functions. Unfortunately, its
performance is highly sensitive to a penalty parameter, which makes ADMM often
unreliable and hard to automate for a non-expert user. We tackle this weakness
of ADMM by proposing a method to adaptively tune the penalty parameters to
achieve fast convergence. The resulting adaptive ADMM (AADMM) algorithm,
inspired by the successful Barzilai-Borwein spectral method for gradient
descent, yields fast convergence and relative insensitivity to the initial
stepsize and problem scaling.
