Incorporating History and Deviations in Forward--Backward Splitting

Hamed Sadeghi, Sebastian Banert, Pontus Giselsson

Published 2022-08-10Version 1

We propose a novel variation of the forward--backward splitting method for solving structured monotone inclusions that incorporates past iterates as well as two deviation vectors into the update equations. The deviation vectors bring a great flexibility to the algorithm and can be chosen arbitrarily as long as they jointly satisfy a norm condition. The method is derived from a Lyapunov analysis from which we conclude convergence rates for various quantities. For a specific choice of the parameters and the deviations, our algorithm reduces to the Halpern iteration and the accelerated proximal point method that both converge as O(1/n^2) in squared norm of the fixed-point residual.