A Relaxed Inertial Forward-Backward-Forward Algorithm for Solving Monotone Inclusions with Application to GANs

Radu Ioan Bot; Michael Sedlmayer; Tu Vuong Phan

Title

Author

Radu Ioan Bot

Faculty of Mathematics, University of Vienna

Michael Sedlmayer

Research Platform Data Science @ Uni Vienna, Research Platforms, University of Vienna

Tu Vuong Phan

Mathematical Sciences, University of Southampton

Abstract

We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims to extend Tseng's forward-backward-forward method by both using inertial effects as well as relaxation parameters. We formulate first a second order dynamical system that approaches the solution set of the monotone inclusion problem to be solved and provide an asymptotic analysis for its trajectories. We provide for RIFBF, which follows by explicit time discretization, a convergence analysis in the general monotone case as well as when applied to the solving of pseudo-monotone variational inequalities. We illustrate the proposed method by applications to a bilinear saddle point problem, in the context of which we also emphasize the interplay between the inertial and the relaxation parameters, and to the training of Generative Adversarial Networks (GANs).

Keywords

forward-backward-forward algorithminertial effectsrelaxation parameterscontinuous time approachapplication to GANs

Object type

journal article

Language

English [eng]

Persistent identifier

phaidra.univie.ac.at/o:2068835

URI

https://jmlr.org/papers/v24/20-267.html

Appeared in

Title