A Relaxed Inertial Forward-Backward-Forward Algorithm for Solving Monotone Inclusions with Application to GANs
Authors: Radu I. Bot, Michael Sedlmayer, Phan Tu Vuong; Published: 24(8):1−37, 2023.
Abstract
This paper presents the relaxed inertial forward-backward-forward (RIFBF) splitting algorithm, which is designed to solve the problem of finding the zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. The algorithm extends Tseng’s forward-backward-forward method by incorporating both inertial effects and relaxation parameters. We formulate a second-order dynamical system to approximate the solution set of the monotone inclusion problem, and provide an asymptotic analysis of its trajectories. The convergence analysis of RIFBF, obtained through explicit time discretization, is presented for the general monotone case as well as for solving pseudo-monotone variational inequalities. Additionally, we demonstrate the effectiveness of the proposed method through applications to a bilinear saddle point problem, highlighting the interplay between the inertial and relaxation parameters, as well as to the training of Generative Adversarial Networks (GANs).
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