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The Alternating Direction Method of Multipliers (ADMM) has gained significantattention across a broad spectrum of machine learning applications.Incorporating the over-relaxation technique shows potential for enhancing theconvergence rate of ADMM. However, determining optimal algorithmic parameters,including both the associated penalty and relaxation parameters, often relieson empirical approaches tailored to specific problem domains and contextualscenarios. Incorrect parameter selection can significantly hinder ADMM'sconvergence rate. To address this challenge, in this paper we first propose ageneral approach to optimize the value of penalty parameter, followed by anovel closed-form formula to compute the optimal relaxation parameter in thecontext of linear quadratic problems (LQPs). We then experimentally validateour parameter selection methods through random instantiations and diverseimaging applications, encompassing diffeomorphic image registration, imagedeblurring, and MRI reconstruction.

Optimizing ADMM and Over-Relaxed ADMM Parameters for Linear Quadratic Problems