An optimized extrapolated proximal gradient method is studied and relations to proximal quasi-Newton methods are revealed. The generic form of the proposed update scheme is related to the accelerated proximal gradient method (also known as FISTA), however we adapt the extrapolation parameter locally. Convergence is proved in a general non-convex setting. Using the equivalence to proximal quasi-Newton methods, new convergence guarantees for these methods are obtained.

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) .

Authors:

Peter Ochs (Saarland University)

Thomas Pock (Graz University of Technology)

Keywords:

accelerated proximal descent, non-smooth optimization, proximal quasi-newton