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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 paper we focus on the convergence analysis of the forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces when the objective function is the sum of two convex functions. Assuming that one of…

Optimization and Control · Mathematics 2016-10-17 J. Y. Bello Cruz , T. T. A. Nghia

A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…

Optimization and Control · Mathematics 2013-02-14 Patrick L. Combettes

We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…

Optimization and Control · Mathematics 2020-09-29 Minh N. Bùi , Patrick L. Combettes

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…

Optimization and Control · Mathematics 2015-07-06 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

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

In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to a vector subspace, a maximally monotone, a monotone-Lipschitzian, and a cocoercive…

Optimization and Control · Mathematics 2022-02-08 Luis M. Briceño-Arias , Jinjian Chen , Fernando Roldán , Yuchao Tang

We propose a new primal-dual splitting method for solving composite inclusions involving Lipschitzian, and parallel-sum-type monotone operators. Our approach extends the framework in \cite{Siopt4} to a more general class of monotone…

Optimization and Control · Mathematics 2015-07-28 Quoc Tran-Dinh , 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 proximal extrapolated gradient method \cite{Malitsky18a} is an extension of the projected reflected gradient method \cite{Malitsky15}. Both methods were proposed for solving the classic variational inequalities. In this paper, we…

Optimization and Control · Mathematics 2019-08-19 Volkan Cevher , Bang Cong Vu

We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…

Optimization and Control · Mathematics 2015-02-23 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

Optimization and Control · Mathematics 2024-01-11 Vu Cong Bang , Dimitri Papadimitriou , Vu Xuan Nham

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

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Optimization and Control · Mathematics 2023-02-27 Laurent Condat , Daichi Kitahara , Andrés Contreras , Akira Hirabayashi

In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradient and the other being partly smooth relative to an active…

Optimization and Control · Mathematics 2015-03-11 Jingwei Liang , Jalal Fadili , Gabriel Peyré

In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…

Optimization and Control · Mathematics 2018-05-31 Luis Briceño-Arias , Sergio López Rivera

The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…

Optimization and Control · Mathematics 2019-11-12 Daniel Reem , Simeon Reich , Alvaro De Pierro

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

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

Optimization and Control · Mathematics 2018-03-26 Yu. Malitsky