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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 work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…

Optimization and Control · Mathematics 2020-06-17 Ernö Robert Csetnek , Yura Malitsky , Matthew K. Tam

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu

In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of…

Optimization and Control · Mathematics 2022-07-14 Francisco J. Aragón-Artacho , Yura Malitsky , Matthew K. Tam , David Torregrosa-Belén

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

Optimization and Control · Mathematics 2019-12-05 Xiaokai Chang , Sanyang Liu , Jianchao Bai , Jun Yang

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 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

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 a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility…

Optimization and Control · Mathematics 2023-07-14 Hamed Sadeghi , Sebastian Banert , Pontus Giselsson

In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…

Optimization and Control · Mathematics 2016-01-13 Jose Yunier Bello Cruz

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…

Optimization and Control · Mathematics 2024-10-01 Tan Nhat Pham , Minh N. Dao , Rakibuzzaman Shah , Nargiz Sultanova , Guoyin Li , Syed Islam

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 approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with…

Optimization and Control · Mathematics 2015-04-23 Sebastian Banert , Radu Ioan Bot

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

Optimization and Control · Mathematics 2026-04-20 Minh N. Dao , Matthew K. Tam , Thang D. Truong

Tseng's algorithm finds a zero of the sum of a maximally monotone operator and a monotone continuous operator by evaluating the latter twice per iteration. In this paper, we modify Tseng's algorithm for finding a zero of the sum of three…

Optimization and Control · Mathematics 2018-03-26 Luis M. Briceño-Arias , Damek Davis

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan

In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical…

Optimization and Control · Mathematics 2016-10-17 Puya Latafat , Panagiotis Patrinos

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…

Optimization and Control · Mathematics 2015-01-30 Yu. V. Malitsky , V. V. Semenov

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

Optimization and Control · Mathematics 2025-03-18 Radu Ioan Boţ , Guoyin Li , Min Tao

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