Preconditioned ADMM with nonlinear operator constraint [link to software] [download software (4 MB)]

Martin Benning, Florian Knoll, Carola-Bibiane Schönlieb and Tuomo Valkonen

Abstract: We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI).

Reference: Martin Benning, Florian Knoll, Carola-Bibiane Schönlieb und Tuomo Valkonen, Preconditioned ADMM with nonlinear operator constraint, IFIP conference proceedings 2015.