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We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…

Optimization and Control · Mathematics 2024-11-20 Patrick L. Combettes

Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for…

Optimization and Control · Mathematics 2020-09-29 Hui Yu , Chunxiang Zong , Yuchao Tang

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian…

Optimization and Control · Mathematics 2014-02-24 Radu Ioan Bot , Ernö Robert Csetnek

Operator splitting schemes have been successfully used in computational sciences to reduce complex problems into a series of simpler subproblems. Since 1950s, these schemes have been widely used to solve problems in PDE and control.…

Optimization and Control · Mathematics 2015-04-07 Damek Davis , Wotao Yin

In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…

Optimization and Control · Mathematics 2026-05-14 Minh N. Dao , Hung M. Phan , Matthew K. Tam , Thang D. Truong

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

Optimization and Control · Mathematics 2022-02-22 Francisco J. Aragón-Artacho , Radu I. Boţ , David Torregrosa-Belén

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator…

Optimization and Control · Mathematics 2025-06-10 Liqian Qin , Yaxuan Zhang , Qiao-Li Dong , Michael Th. Rassias

The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…

Optimization and Control · Mathematics 2018-05-28 R. Díaz Millán

In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed…

Optimization and Control · Mathematics 2022-07-20 Luis Briceño-Arias , Fernando Roldán

We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…

Optimization and Control · Mathematics 2013-08-14 Dinh 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

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…

Optimization and Control · Mathematics 2010-11-29 L. Briceno-Arias , P. L. Combettes

In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each iteration of these algorithms require one forward evaluation…

Optimization and Control · Mathematics 2020-01-22 Janosch Rieger , Matthew K. Tam

In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each…

Optimization and Control · Mathematics 2025-11-19 Liqian Qin , Aviv Gibali , Cuijie Zhang , Yuchao Tang

This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…

Optimization and Control · Mathematics 2025-10-03 Anshika Anshika , Jiaxing Li , Debdas Ghosh , Xiangxiong Zhang

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

Optimization and Control · Mathematics 2016-09-28 Li Shen , Shaohua Pan

Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…

Quantum Physics · Physics 2025-10-16 Matteo Vandelli , Francesco Ferrari , Daniele Dragoni

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their…

Optimization and Control · Mathematics 2014-02-11 Hugo Raguet , Jalal Fadili , Gabriel Peyré

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

In this paper, we propose an adaptive forward-backward-forward splitting algorithm for finding a zero of a pseudo-monotone operator which is split as a sum of three operators: the first is continuous single-valued, the second is…

Optimization and Control · Mathematics 2025-03-04 Flavia Chorobura , Ion Necoara , Jean-Christophe Pesquet