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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

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

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the…

Optimization and Control · Mathematics 2011-08-09 Patrick L. Combettes , Jean-Christophe Pesquet

We introduce a dynamical system to the problem of finding zeros of the sum of two maximally monotone operators. We investigate the existence, uniqueness and extendability of solutions to this dynamical system in a Hilbert space. We prove…

Classical Analysis and ODEs · Mathematics 2021-08-17 Ewa M. Bednarczuk , Raj Narayan Dhara , Krzysztof E. Rutkowski

We propose and study a weakly convergent variant of the forward--backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector which provides additional degrees of freedom.…

Optimization and Control · Mathematics 2022-08-15 Hamed Sadeghi , Sebastian Banert , Pontus Giselsson

A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous.…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Jonathan Eckstein

In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…

Optimization and Control · Mathematics 2023-11-10 Emilie Chouzenoux , Jean-Christophe Pesquet , Fernando Roldán

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 investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7].…

Optimization and Control · Mathematics 2012-11-09 Radu Ioan Bot , Christopher Hendrich

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

Optimization and Control · Mathematics 2022-07-21 Olaniyi S. Iyiola , Yekini Shehu

In this paper, we propose a stochastic version of the classical Tseng's forward-backward-forward method with inertial term for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued monotone operator…

Optimization and Control · Mathematics 2022-02-22 Van Dung Nguyen , Nguyen The Vinh

In this paper we propose a resolvent splitting with minimal lifting for finding a zero of the sum of $n\ge 2$ maximally monotone operators involving the composition with a linear bounded operator. The resolvent of each monotone operator,…

Optimization and Control · Mathematics 2022-07-28 Luis M. Briceño-Arias

We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert…

Functional Analysis · Mathematics 2014-07-02 Radu Ioan Bot , Ernö Robert Csetnek

We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…

Optimization and Control · Mathematics 2017-05-02 Saverio Salzo

Consider the problem of finding a zero of a finite sum of maximally monotone operators, where some operators are Lipschitz continuous and the rest are potentially set-valued. We propose a forward-backward-type algorithm for this problem…

Optimization and Control · Mathematics 2025-12-16 Matthew K Tam , Liam Timms , Lele Zhang

We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Chinedu Izuchukwu , Chibueze Christian Okeke

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 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

We propose a new class of primal-dual Fejer monotone algorithms for solving systems of com- posite monotone inclusions. Our construction is inspired by a framework used by Eckstein and Svaiter for the basic problem of finding a zero of the…

Optimization and Control · Mathematics 2014-10-07 Abdullah Alotaibi , Patrick L. Combettes , N. Shahzad

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…

Functional Analysis · Mathematics 2013-07-30 Radu Ioan Bot , Christopher Hendrich