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We propose a new class of inertial proximal alternating direction method of multipliers (ADMMs), which unifies inertial proximal point method and proximal ADMM. The proposed algorithmic framework is very general in the sense that the weighting matrices in the proximal terms can be only positive semidefinite. We established convergence as well as asymptotic o(1/k) and nonasymptotic O(1/k) rates of convergence for the best primal function value and feasibility residues.
This presentation is part of Minisymposium “MS59 - Approaches for fast optimisation in imaging and inverse problems (3 parts)”
organized by: Jingwei Liang (University of Cambridge) , Carola-Bibiane Schönlieb (University of Cambridge) , Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay) .