# Fast convergence of generalized forward-backward algorithms for structured monotone inclusions

@inproceedings{Mainge2021FastCO, title={Fast convergence of generalized forward-backward algorithms for structured monotone inclusions}, author={Paul-Emile Maing'e}, year={2021} }

In this paper, we develop rapidly convergent forward-backward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forward-backward method for two general operators is first considered, by incorporating an inertial term (closed 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 (xn…

## 2 Citations

Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions

- Computer Science, Mathematics
- 2021

A new type of accelerated algorithms to solve some classes of maximally monotones equations as well as monotone inclusions using a so-called Halpern-type fixed-point iteration to solve convex-concave minimax problems and a new accelerated DR scheme to derive a new variant of the alternating direction method of multipliers (ADMM).

The Connection Between Nesterov's Accelerated Methods and Halpern Fixed-Point Iterations

- Mathematics
- 2022

We derive a direct connection between Nesterov’s accelerated first-order algorithm and the Halpern fixed-point iteration scheme for approximating a solution of a co-coercive equation. We show that…

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