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Preconditioned ADMM with nonlinear operator constraint

Accepted version
Peer-reviewed

Type

Article

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Authors

Benning, Martin 
Knoll, Florian 
Schonlieb, Carola-Bibiane 
Valkonen, Tuomo 

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).

Description

This is the author accepted manuscript. The final version is available from Springer via https://doi.org/10.1007/978-3-319-55795-3_10.

Keywords

ADMM, primal-dual, nonlinear inverse problems, parallel MRI, proximal point method, operator splitting, iterative Bregman method

Journal Title

IFIP Advances in Information and Communication Technology

Conference Name

Journal ISSN

Volume Title

494

Publisher

Springer
Sponsorship
MB, CS and TV acknowledge EPSRC grant EP/M00483X/1. FK ackowledges National Institutes of Health grant NIH P41 EB017183.
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