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

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