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Employing the ideas of nonlinear preconditioning and testing of the proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple iteration-wise inequality. When applied to fixed-point operators, the latter can be seen as a generalisation of firm non-expansivity or the α-averaged property. In this talk we demonstrate the effectiveness of the general approach on several classical algorithms, as well as their stochastic variants.
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) .