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This paper provides a new way of developing the splitting method which is used to solve the problem of finding the resolvent of the sum of maximal monotone operators in Hilbert spaces. By employing accelerated techniques developed by Davis…

Optimization and Control · Mathematics 2018-09-13 Shin-ya Matsushita

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 how to replace the fundamental…

Optimization and Control · Mathematics 2020-08-24 Patrick R. Johnstone , Jonathan Eckstein

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

Optimization and Control · Mathematics 2021-02-18 Nguyen Van Dung , Bang Cong Vu

In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…

Optimization and Control · Mathematics 2026-05-19 Haowen Zheng , Yongyu Fu , Qiao-Li Dong , Shuangbao Li

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

Optimization and Control · Mathematics 2012-06-29 Patrick L. Combettes , Bang C. Vũ

We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of…

Optimization and Control · Mathematics 2025-07-09 M. Marques Alves , J. E. Navarro Caballero , R. T. Marcavillaca

We study the convergence of a Douglas-Rachford type splitting algorithm for the infinite dimensional stochastic differential equation $$dX+A(t)(X)dt=X\,dW\mbox{ in }(0,T);\ X(0)=x,$$ where $A(t):V\to V'$ is a nonlinear, monotone, coercive…

Probability · Mathematics 2018-06-18 Viorel Barbu , Michael Röckner

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits…

Optimization and Control · Mathematics 2023-01-25 M. Marques Alves , Marina Geremia , Raul T. Marcavillaca

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…

Optimization and Control · Mathematics 2017-11-07 Renato D. C. Monteiro , Chee-Khian Sim

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…

Numerical Analysis · Mathematics 2026-04-02 Fernando Casas , Ander Murua

The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We…

Optimization and Control · Mathematics 2016-08-09 Walaa M. Moursi

In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…

Optimization and Control · Mathematics 2020-06-17 Ernö Robert Csetnek , Yura Malitsky , Matthew K. Tam

In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…

Optimization and Control · Mathematics 2021-12-08 Quoc Tran-Dinh , Yang Luo

Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…

Dynamical Systems · Mathematics 2023-09-01 Andreas Bartel , Malak Diab , Andreas Frommer , Michael Günther

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu

Monotone operator splitting is a powerful paradigm that facilitates parallel processing for optimization problems where the cost function can be split into two convex functions. We propose a generalized form of monotone operator splitting…

Optimization and Control · Mathematics 2018-11-13 Kenta Niwa , W. Bastiaan Kleijn

In this paper we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another…

Functional Analysis · Mathematics 2014-07-02 Sebastian Banert , Radu Ioan Bot

This paper describes the Conic Operator Splitting Method (COSMO) solver, an operator splitting algorithm for convex optimisation problems with quadratic objective function and conic constraints. At each step the algorithm alternates between…

Optimization and Control · Mathematics 2021-08-31 Michael Garstka , Mark Cannon , Paul Goulart

We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…

Optimization and Control · Mathematics 2015-12-15 Radu Ioan Bot , Ernö Robert Csetnek

In this work, we propose a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators. Our method converges under the same assumptions as Tseng's forward-backward-forward method,…

Optimization and Control · Mathematics 2020-05-08 Yura Malitsky , Matthew K. Tam
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