Tuning Over-Relaxed ADMM
This provides a theoretical improvement for parameter tuning in ADMM, though it appears incremental as it builds directly on prior work.
The paper tackles the problem of tuning parameters for over-relaxed ADMM by deriving explicit formulas from an SDP solution, enabling optimal parameter selection for arbitrary strongly convex objective functions.
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program (SDP). In the case of over-relaxed Alternating Direction Method of Multipliers (ADMM), an explicit and closed form solution to this SDP was derived in our recent work [1]. The purpose of this paper is twofold. First, we summarize these results. Second, we explore one of its consequences which allows us to obtain general and simple formulas for optimal parameter selection. These results are valid for arbitrary strongly convex objective functions.