  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).
