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We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…

Optimization and Control · Mathematics 2018-07-31 Nimit Nimana , Narin Petrot

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

In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method…

Optimization and Control · Mathematics 2025-11-07 Liqian Qin , Yuchao Tang , Jigen Peng

We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact…

Optimization and Control · Mathematics 2024-06-24 Ewa Bednarczuk , Giovanni Bruccola , Gabriele Scrivanti , The Hung Tran

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

A stochastic Forward-Backward algorithm with a constant step is studied. At each time step, this algorithm involves an independent copy of a couple of random maximal monotone operators. Defining a mean operator as a selection integral, the…

Optimization and Control · Mathematics 2018-04-05 Pascal Bianchi , Walid Hachem , Adil Salim

This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…

Optimization and Control · Mathematics 2021-06-15 Pankaj Gautam , D. R. Sahu , J. C. Yao

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

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 begin by considering second order dynamical systems of the from $\ddot x(t) + \gamma(t)\dot x(t) + \lambda(t)B(x(t))=0$, where $B: {\cal H}\rightarrow{\cal H}$ is a cocoercive operator defined on a real Hilbert space ${\cal H}$,…

Optimization and Control · Mathematics 2016-03-10 Radu Ioan Bot , Ernö Robert Csetnek

We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the…

Optimization and Control · Mathematics 2026-01-23 Felipe Atenas , Minh N. Dao , Matthew K. Tam

In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng's…

Optimization and Control · Mathematics 2021-04-28 Yunier Bello-Cruz , Oday Hazaimah

We present a novel matrix-parametrized frugal splitting algorithm which finds the zero of a sum of maximal monotone and cocoercive operators composed with linear selection operators. We also develop a semidefinite programming framework for…

Optimization and Control · Mathematics 2025-07-29 Peter Barkley , Robert L. Bassett

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

Exactly Solvable and Integrable Systems · Physics 2007-11-16 Dan Butnariu , Gabor Kassay

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 Lipschitz continuous operator. This work aims…

Optimization and Control · Mathematics 2020-03-24 Radu Ioan Bot , Michael Sedlmayer , Phan Tu Vuong

In this article, we study inertial algorithms for numerically solving monotone inclusions involving the sum of a maximally monotone and a cocoercive operator. In particular, we analyze the convergence of inertial and relaxed versions of the…

Optimization and Control · Mathematics 2024-12-04 Fernando Roldán , Cristian Vega

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 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

This article introduces a novel approach to learning monotone neural networks through a newly defined penalization loss. The proposed method is particularly effective in solving classes of variational problems, specifically monotone…

Optimization and Control · Mathematics 2025-03-07 Younes Belkouchi , Jean-Christophe Pesquet , Audrey Repetti , Hugues Talbot

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…

Optimization and Control · Mathematics 2012-06-27 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich