ADMM Penalty Parameter Selection by Residual Balancing
This work addresses a key problem in optimization algorithms for researchers and practitioners using ADMM, though it is incremental as it modifies an existing heuristic.
The paper identifies a serious flaw in a heuristic method for selecting the penalty parameter in ADMM, which is crucial for performance, and proposes a modification to partially address this issue.
Appropriate selection of the penalty parameter is crucial to obtaining good performance from the Alternating Direction Method of Multipliers (ADMM). While analytic results for optimal selection of this parameter are very limited, there is a heuristic method that appears to be relatively successful in a number of different problems. The contribution of this paper is to demonstrate that their is a potentially serious flaw in this heuristic approach, and to propose a modification that at least partially addresses it.