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).
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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⟩

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