• Corpus ID: 236155035

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… 
View PDF on arXiv
2 Citations
Highly Influential Citations
2
Background Citations
2
Methods Citations
2
Results Citations
1

2 Citations

Citation Type

Citation Type

Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions
TLDR
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
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…

References

SHOWING 1-10 OF 55 REFERENCES
An Inertial Forward-Backward Algorithm for Monotone Inclusions
  • D. Lorenz, T. Pock
  • Mathematics, Computer Science
    Journal of Mathematical Imaging and Vision
  • 2014
TLDR
An inertial forward-backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive, inspired by the accelerated gradient method of Nesterov.
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
  • P. Tseng
  • Mathematics
    SIAM J. Control. Optim.
  • 2000
TLDR
A modification to the forward-backward splitting method for finding a zero of the sum of two maximal monotone mappings is proposed, under which the method converges assuming only the forward mapping is (Lipschitz) continuous on some closed convex subset of its domain.
Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators
We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying…
Accelerated and Inexact Forward-Backward Algorithms
We propose a convergence analysis of accelerated forward-backward splitting methods for composite function minimization, when the proximity operator is not available in closed form, and can only be…
A Reflected Forward-Backward Splitting Method for Monotone Inclusions Involving Lipschitzian Operators
In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real…
A Relaxed Inertial Forward-Backward-Forward Algorithm for Solving Monotone Inclusions with Application to GANs
We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and…
Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators
TLDR
This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods and the application to convex minimization problems is given special attention.
A Generalized Proximal Point Algorithm and Its Convergence Rate
TLDR
This work proposes a generalized proximal point algorithm in the generic setting of finding a root of a maximal monotone operator and establishes the convergence rate of this generalized PPA scheme under different conditions.
A Generalized Forward-Backward Splitting
TLDR
This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form F + G_i, and proves its convergence in infinite dimension, and its robustness to errors on the computation of the proximity operators and of the gradient of $F$.
On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators
TLDR
This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm, which allows the unification and generalization of a variety of convex programming algorithms.
...
1
2
3
4
5
...