Transfer of Improvement Strategies Between DRS and ADMM: A Unified Classification Framework

Abstract

Douglas-Rachford splitting (DRS) and the alternating direction method of multipliers (ADMM) are two fundamental first-order methods for structured convex optimization. Although derived from different viewpoints, ADMM can be interpreted as the application of DRS to the dual problem. Based on this structural equivalence, this paper studies how algorithmic improvement strategies can be transferred between the two methods. We classify transferable strategies into three categories: exact operator-level transfer, parameter-driven transfer, and heuristic transfer. Representative examples including relaxation, metric scaling, adaptive parameter updates, and residual balancing are discussed to illustrate the different levels of transferability. This perspective provides a systematic way to understand the relationship between DRS and ADMM and clarifies how algorithmic ideas developed for one method may inform the design of variants of the other, offering a unified framework that both explains existing variants and guides the design of new ones.