Relaxing Alternating Direction Method of Multipliers (ADMM) for Linear Inverse Problems

Abstract

We investigate the Alternating Direction Method of Multipliers (ADMM) for solving linear inverse problems. In particular, a relaxing factor is introduced to the standard algorithm allowing more flexible updating of the Lagrange multiplier. The convergence result is established for the Relaxing ADMM for the noise free data under appropriate assumptions. We also calibrate the convergence of the algorithm for the noisy data when noise vanishes by a modified discrepancy principle.