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We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…

Optimization and Control · Mathematics 2026-01-22 Santanu Soe , V. Vetrivel , Jen-Chih Yao

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

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 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

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…

Functional Analysis · Mathematics 2026-03-19 Watanjeet Singh , Sumit Chandok

We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…

Optimization and Control · Mathematics 2023-12-20 Radu Ioan Bot , Dang-Khoa Nguyen , Chunxiang Zong

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 a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belongs to the fixed point set…

Optimization and Control · Mathematics 2021-11-02 Luis Briceño-Arias , Julio Deride , Sergio López-Rivera , Francisco J. Silva

In this paper, based on a double inertial extrapolation steps strategy and relaxation techniques, we introduce a new Tseng splitting method with double inertial extrapolation steps and self-adaptive step sizes for solving monotone inclusion…

Optimization and Control · Mathematics 2022-09-27 Zhong-bao Wang , Zhen-yin Lei , Xin Long , Zhang-you Chen

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

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 study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundational result by Ryu, we fully characterize all methods that…

Optimization and Control · Mathematics 2025-04-16 Anton Åkerman , Enis Chenchene , Pontus Giselsson , Emanuele Naldi

We propose and study the weak convergence of a projective splitting algorithm for solving multi-term composite monotone inclusion problems involving the finite sum of $n$ maximal monotone operators, each of which having an inner four-block…

Optimization and Control · Mathematics 2024-05-08 M. Marques Alves

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

We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…

Optimization and Control · Mathematics 2013-06-25 Marc Lassonde , Ludovic Nagesseur

In this paper, we propose an improved iterative method for solving the monotone inclusion problem in the form of $0 \in Ax + Dx + N_{C}(x)$ in real Hilbert space, where $A$ is a maximally monotone operator, $D$ and $B$ are monotone and…

Optimization and Control · Mathematics 2023-06-30 Buris Tongnoi

We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and…

Optimization and Control · Mathematics 2021-03-12 Minh N. Bùi , Patrick L. Combettes

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

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

Optimization and Control · Mathematics 2017-11-29 Regina S. Burachik , R. Díaz Millán

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Optimization and Control · Mathematics 2020-08-31 Zheng Zhou , Bing Tan , Songxiao Li