Preconditioned ADMM with Nonlinear Operator Constraint

Martin Benning, Florian Knoll, Carola-Bibiane Schönlieb, 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).