DWIFOB: A Dynamically Weighted Inertial Forward-Backward Algorithm for Monotone Inclusions

TL;DR

This paper introduces DWIFOB, a new inertial forward-backward algorithm with dynamic weighting and extrapolation, demonstrating superior robustness and performance in solving structured monotone inclusion problems compared to existing methods.

Contribution

The paper presents a novel dynamically weighted inertial forward-backward algorithm with a primal-dual variant, improving convergence and robustness for monotone inclusion problems.

Findings

Primal-dual DWIFOB outperforms Chambolle-Pock in numerical tests.

DWIFOB is more robust than regularized Anderson acceleration.

The method shows strong convergence and reliability across experiments.

Abstract

We propose a novel dynamically weighted inertial forward-backward algorithm (DWIFOB) for solving structured monotone inclusion problems. The scheme exploits the globally convergent forward-backward algorithm with deviations in [26] as the basis and combines it with the extrapolation technique used in Anderson acceleration to improve local convergence. We also present a globally convergent primal-dual variant of DWIFOB and numerically compare its performance to the primal-dual method of Chambolle-Pock and a Tikhonov regularized version of Anderson acceleration applied to the same problem. In all our numerical evaluations, the primal-dual variant of DWIFOB outperforms the Chambolle-Pock algorithm. Moreover, our numerical experiments suggest that our proposed method is much more robust than the regularized Anderson acceleration, which can fail to converge and be sensitive to algorithm parameters. These numerical experiments highlight that our method performs very well while still being robust and reliable.