Preconditioned ADMM with nonlinear operator constraint
Numerical Analysis
2020-02-13 v1 Optimization and Control
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).
Cite
@article{arxiv.1511.00425,
title = {Preconditioned ADMM with nonlinear operator constraint},
author = {Martin Benning and Florian Knoll and Carola-Bibiane Schönlieb and Tuomo Valkonen},
journal= {arXiv preprint arXiv:1511.00425},
year = {2020}
}