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We introduce a relaxed inertial forward-backward-forward (RIFBF) splittingalgorithm for approaching the set of zeros of the sum of a maximally monotoneoperator and a single-valued monotone and Lipschitz continuous operator. Thiswork aims to extend Tseng's forward-backward-forward method by both usinginertial effects as well as relaxation parameters. We formulate first a secondorder dynamical system which approaches the solution set of the monotoneinclusion problem to be solved and provide an asymptotic analysis for itstrajectories. We provide for RIFBF, which follows by explicit timediscretization, a convergence analysis in the general monotone case as well aswhen applied to the solving of pseudo-monotone variational inequalities. Weillustrate the proposed method by applications to a bilinear saddle pointproblem, in the context of which we also emphasize the interplay between theinertial and the relaxation parameters, and to the training of GenerativeAdversarial Networks (GANs).

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