Distributed forward-backward methods for ring networks

@article{AragonArtacho2021DistributedFM,
  title={Distributed forward-backward methods for ring networks},
  author={Francisco J. Arag'on-Artacho and Yura Malitsky and Matthew K. Tam and David Torregrosa-Bel'en},
  journal={Computational Optimization and Applications},
  year={2021}
}
In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of the studied algorithms requires one resolvent evaluation per set-valued operator, one forward evaluation per cocoercive operator, and two forward evaluations per monotone operator. Unlike existing methods, the structure of the proposed algorithms are suitable… 

A Framework for Decentralised Resolvent Splitting

A new framework for decentralised resolvent splitting for solving minimisations problems with the form of a zero in the sum of set-valued monotone operators over regular networks is developed.

Frugal and Decentralised Resolvent Splittings Defined by Nonexpansive Operators

A general framework for frugal resolvent splitting is developed which simultaneously covers and extends several important schemes in the literature and yields a new resolent splitting algorithm which is suitable for decentralised implementation on regular networks.

Frugal Splitting Operators: Representation, Minimal Lifting and Convergence

We consider frugal splitting operators for finite sum monotone inclusion problems, i.e., splitting operators that use exactly one direct or resolvent evaluation of each operator of the sum. A novel

References

SHOWING 1-10 OF 26 REFERENCES

A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

This work proposes a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators that does not require cocoercivity of the single-valued operator.

An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator

  • Minh N. DaoH. Phan
  • Mathematics
    Fixed Point Theory and Algorithms for Sciences and Engineering
  • 2021
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and

An adaptive splitting algorithm for the sum of three operators

Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and

Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions

Resolvent Splitting for Sums of Monotone Operators with Minimal Lifting

This work considers the class of algorithms where each resolvent is evaluated only once per iteration and shows that any algorithm from this class is necessarily defined on a d -fold Cartesian product space with d ≥ n − 1.

Projective splitting with forward steps

This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show

Parallel and Distributed Computation: Numerical Methods

This work discusses parallel and distributed architectures, complexity measures, and communication and synchronization issues, and it presents both Jacobi and Gauss-Seidel iterations, which serve as algorithms of reference for many of the computational approaches addressed later.

A Generalized Forward-Backward Splitting

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 $F$.

Shadow Douglas–Rachford Splitting for Monotone Inclusions

This algorithm naturally arises from a non-standard discretization of a continuous dynamical system associated with the Douglas–Rachford splitting algorithm by performing an explicit, rather than implicit, discretized with respect to one of the operators involved.

A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting

This work establishes the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting, which reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators.