Preconditioned ADMM with nonlinear operator constraint

Benning, Martin ; Knoll, Florian ; Schonlieb, Carola-Bibiane ; Valkonen, Tuomo (2016)


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).