English
Related papers

Related papers: Dynamical system related to primal-dual splitting …

200 papers

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

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

In this paper we present a novel derivation for an existing node-based algorithm for distributed optimisation termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, in this work monotone operator theory…

Optimization and Control · Mathematics 2017-11-07 Thomas Sherson , Richard Heusdens , W. Bastiaan Kleijn

The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we…

Optimization and Control · Mathematics 2025-11-07 Jan Harold Alcantara , Akiko Takeda

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

Optimization and Control · Mathematics 2018-04-19 Laurentiu Leustean , Adriana Nicolae , Andrei Sipos

The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well…

Optimization and Control · Mathematics 2020-04-14 Minh N. Dao , Hung M. Phan

A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…

Numerical Analysis · Mathematics 2023-09-26 Andreas Bartel , Michael Günther , Birgit Jacob , Timo Reis

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…

Optimization and Control · Mathematics 2009-02-26 H. Attouch , L. M. Briceno-Arias , P. L. Combettes

In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a priori information set is represented by the intersection of fixed point sets of a finite…

Optimization and Control · Mathematics 2020-11-06 Luis Briceño-Arias , Julio Deride , Cristian Vega

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 consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…

Optimization and Control · Mathematics 2016-04-19 Meng Wen , Shigang Yue , Yuchao Tang , Jigen Peng

In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each iteration of these algorithms require one forward evaluation…

Optimization and Control · Mathematics 2020-01-22 Janosch Rieger , Matthew K. Tam

This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…

Optimization and Control · Mathematics 2022-04-12 Hao Luo

We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible…

Optimization and Control · Mathematics 2011-11-10 Minh Dang Doan , Tamás Keviczky , Bart De Schutter

In this paper, in the setting of Hilbert spaces, we consider a Tikhonov regularized second-order plus first-order primal-dual dynamical system with asymptotically vanishing damping for a linear equality constrained convex optimization…

Optimization and Control · Mathematics 2024-04-23 Ting Ting Zhu , Rong Hu , Ya Ping Fang

This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and…

Optimization and Control · Mathematics 2025-09-16 Hadi Abbaszadehpeivasti , Moslem Zamani

In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…

Optimization and Control · Mathematics 2026-05-19 Haowen Zheng , Yongyu Fu , Qiao-Li Dong , Shuangbao Li

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…

Optimization and Control · Mathematics 2017-11-21 Radu Ioan Bot , Ernö Robert Csetnek , Dennis Meier

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

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…

Numerical Analysis · Mathematics 2008-04-22 N. S. Hoang , A. G. Ramm