Preconditioned ADMM with nonlinear operator constraint

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).

References in corpus (1)

• Variable metric inexact line-search based methods for nonsmooth optimization

Cited by in corpus (6)

• Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior
• Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization
• ParticLS: Object-oriented software for discrete element methods and peridynamics
• Distributed and Scalable Optimization for Robust Proton Treatment Planning
• First-order primal-dual methods for nonsmooth nonconvex optimisation
• Quantitative MR Image Reconstruction using Parameter-Specific Dictionary Learning with Adaptive Dictionary-Size and Sparsity-Level Choice