Preconditioned Proximal-Point Methods for Imaging ApplicationsMS59

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) .

Tuomo Valkonen (University of Liverpool)