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Related papers: Bregman three-operator splitting methods

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We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

Optimization and Control · Mathematics 2021-04-20 Yuzixuan Zhu , Deyi Liu , Quoc Tran-Dinh

We study Bregman proximal augmented Lagrangian methods with second-order oracles for convex convex-composite optimization problems. The outer loop is an instance of the Bregman proximal point algorithm with relative errors in the sense of…

Optimization and Control · Mathematics 2026-02-18 Emanuel Laude

Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this paper, we propose the Bregman parallel direction method of…

Optimization and Control · Mathematics 2018-05-03 Yue Yu , Behçet Açıkmeşe , Mehran Mesbahi

In this paper, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-02-20 Richard Heusdens , Guoqiang Zhang

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…

Optimization and Control · Mathematics 2021-06-30 Xin He , Rong Hu , Ya-Ping Fang

The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting…

Optimization and Control · Mathematics 2025-12-12 Max Nilsson , Anton Åkerman , Pontus Giselsson

We propose a novel algorithmic framework of Variable Metric Over-Relaxed Hybrid Proximal Extra-gradient (VMOR-HPE) method with a global convergence guarantee for the maximal monotone operator inclusion problem. Its iteration complexities…

Optimization and Control · Mathematics 2019-06-03 Li Shen , Peng Sun , Yitong Wang , Wei Liu , Tong Zhang

In this work we propose a stochastic primal-dual three-operator splitting algorithm (TOS-SPDHG) for solving a class of convex three-composite optimization problems. Our proposed scheme is a direct three-operator splitting extension of the…

Optimization and Control · Mathematics 2025-03-18 Junqi Tang , Matthias Ehrhardt , Carola-Bibiane Schönlieb

We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a…

Optimization and Control · Mathematics 2020-09-25 Stanislav Mazurenko , Jyrki Jauhiainen , Tuomo Valkonen

In this paper, a centralized two-block separable optimization is considered for which a fully parallel primal-dual discrete-time algorithm with fixed step size is derived based on monotone operator splitting method. In this algorithm, the…

Optimization and Control · Mathematics 2020-09-30 S. Sh. Alaviani , A. G. Kelkar

We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…

Optimization and Control · Mathematics 2014-11-11 Tor Myklebust , Levent Tunçel

The Condat-V\~u algorithm is a widely used primal-dual method for optimizing composite objectives of three functions. Several algorithms for optimizing composite objectives of two functions are special cases of Condat-V\~u, including…

Optimization and Control · Mathematics 2024-03-27 Derek Driggs , Matthias J. Ehrhardt , Carola-Bibiane Schönlieb , Junqi Tang

We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…

Optimization and Control · Mathematics 2024-10-04 Ignace Loris , Simone Rebegoldi

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…

Optimization and Control · Mathematics 2012-06-27 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-16 Richard Heusdens , Guoqiang Zhang

In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-02-06 G. Zhang , R. Heusdens

This paper develops a distributed primal-dual algorithm via event-triggered mechanism to solve a class of convex optimization problems subject to local set constraints, coupled equality and inequality constraints. Different from some…

Optimization and Control · Mathematics 2022-10-27 Yi Huang , Xianlin Zeng , Ziyang Meng , Jian Sun

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

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian…

Optimization and Control · Mathematics 2014-02-24 Radu Ioan Bot , Ernö Robert Csetnek

In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however…

Optimization and Control · Mathematics 2012-12-04 Radu Ioan Bot , Christopher Hendrich