Preconditioned ADMM with Nonlinear Operator Constraint

  title={Preconditioned ADMM with Nonlinear Operator Constraint},
  author={Martin Benning and Florian Knoll and Carola-Bibiane Schoenlieb and Tuomo Valkonen},
  booktitle={System Modelling and Optimization},
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). 


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Applications of the method of multipliers to variational inequalities

Daniel Gabay
Studies in mathematics and its applications, • 1983
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