
Journal of Convex Analysis 29 (2022), No. 3, 893920 Copyright Heldermann Verlag 2022 Fast Convergence of Generalized ForwardBackward Algorithms for Structured Monotone Inclusions PaulEmile Maingé Université des Antilles, Martinique, France paulemile.mainge@univantilles.fr [Abstractpdf] We develop rapidly convergent forwardbackward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forwardbackward method for two general operators is first considered, by incorporating an inertial term (close to the acceleration techniques introduced by Nesterov), a constant relaxation factor and a correction term. In a Hilbert space setting, we prove the weak convergence to equilibria of the iterates $(x_n)$, with worstcase rates of $o(n^{1})$ in terms of both the discrete velocity and the fixed point residual, instead of the classical rates of ${\cal O}(n^{1/2})$ established so far for related algorithms. Our procedure is then adapted to more general monotone inclusions and a fast primaldual algorithm is proposed for solving convexconcave saddle point problems. Keywords: Nesterovtype algorithm, inertialtype algorithm, global rate of convergence, fast firstorder method, relaxation factors, correction term, accelerated proximal algorithm, fixed point problem. MSC: 90C25, 90C30, 90C60, 68Q25, 49M25. [ Fulltextpdf (211 KB)] for subscribers only. 