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).
https://hal.inria.fr/hal-01626884 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Tuesday, October 31, 2017 - 2:40:04 PM Last modification on : Wednesday, November 3, 2021 - 4:17:33 AM Long-term archiving on: : Thursday, February 1, 2018 - 1:50:50 PM
Florian Knoll, Carola-Bibiane Schönlieb, Tuomo Valkonen, Martin Benning. Preconditioned ADMM with Nonlinear Operator Constraint. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.117-126, ⟨10.1007/978-3-319-55795-3_10⟩. ⟨hal-01626884⟩