Inexact alternating direction method of multipliers (InADMM) for the acceleration of l2-l1 inverse problems Available to Purchase

This paper develops and studies an improved version of the Alternating Direction Method of Multipliers (ADMM), named Inexact ADMM (InADMM), specifically designed for largescale optimization problems. The traditional implementation of ADMM can be challenging when applied to large-scale problems. The latter is particularly true in several largescale seismic applications. One subproblem, the x-update, entails solving a large system of equations in each iteration of the ADMM solver. This research addresses two fundamental questions: the precision required in solving the aforementioned linear system of equations at each nested iteration for assured global convergence and the optimal number of nested iterations. InADMM introduces a novel inexactness criterion based on the structure of the problem. This critical modification automates and streamlines the resolution of nested iterations. We demonstrate the application of InADMM with two classical problems in seismic processing and inversion.