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We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

Optimization and Control · Mathematics 2015-11-30 Patrick L. Combettes , Jonathan Eckstein

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in…

Optimization and Control · Mathematics 2021-07-27 Bing Tan , Jingjing Fan , Songxiao Li

In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories,…

Optimization and Control · Mathematics 2022-10-20 AÏcha Balhag , Zakaria Mazgouri , Michel Théra

The nonlinear, or warped, resolvent recently explored by Giselsson and B\`ui-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents,…

Optimization and Control · Mathematics 2023-10-02 Martin Morin , Sebastian Banert , Pontus Giselsson

We study a forward backward splitting algorithm that solves the variational inequality \begin{equation*} A x +\nabla \Phi(x)+ N_C (x) \ni 0 \end{equation*} where $H$ is a real Hilbert space, $A: H\rightrightarrows H$ is a maximal monotone…

Optimization and Control · Mathematics 2014-08-06 Marc-Olivier Czarnecki , Nahla Noun , Juan Peypouquet

The deviation vectors provide additional degrees of freedom and effectively enhance the flexibility of algorithms. In the literature, the iterative schemes with deviations are constructed and their convergence analyses are performed on an…

Optimization and Control · Mathematics 2025-09-05 Yongyu Fu , Haowen Zheng , Qiao-Li Dong , Xiaolong Qin , Jing Zhao

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 present a forward-backward-based algorithm to minimize a sum of a differentiable function and a nonsmooth function, both being possibly nonconvex. The main contribution of this work is to consider the challenging case where the nonsmooth…

Optimization and Control · Mathematics 2021-02-02 Audrey Repetti , Yves Wiaux

We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's…

Optimization and Control · Mathematics 2025-02-25 Zepeng Wang , Juan Peypouquet

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

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

In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…

Optimization and Control · Mathematics 2015-09-17 Jingwei Liang , Jalal Fadili , Gabriel Peyré

In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is…

Optimization and Control · Mathematics 2025-09-19 Kansei Ushiyama

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…

Optimization and Control · Mathematics 2014-10-28 Jean-Christophe Pesquet , Audrey Repetti

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

We consider the monotone inclusion problem with a sum of 3 operators, in which 2 are monotone and 1 is monotone-Lipschitz. The classical Douglas--Rachford and Forward-backward-forward methods respectively solve the monotone inclusion…

Optimization and Control · Mathematics 2019-10-17 Ernest K. Ryu , Bang Cong Vu

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…

Optimization and Control · Mathematics 2024-09-17 Zheng Zhou , Bing Tan , Songxiao Li

We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's accelerated interpretation. We show that one method is…

Optimization and Control · Mathematics 2026-04-16 Quoc Tran-Dinh

This study explores an inertial-based contraction-type approach for addressing monotone variational inclusion problems (in short, MVIP) within real Hilbert spaces. Most contraction-type techniques assume Lipschitz continuity and…

Optimization and Control · Mathematics 2026-04-09 Feeroz Babu , Syed Shakaib Irfan , Jen-Chih Yao , Xiaopeng Zhao

In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both…

Optimization and Control · Mathematics 2020-11-09 Hedy Attouch , Zaki Chbani , Jalal Fadili , Hassan Riahi