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Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…

Optimization and Control · Mathematics 2017-11-02 Qinghua Liu , Xinyue Shen , Yuantao Gu

Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…

Optimization and Control · Mathematics 2020-08-05 Jiawei Zhang , Zhi-Quan Luo

We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$,…

Signal Processing · Electrical Eng. & Systems 2025-12-23 Atharva Awari , Nicolas Gillis , Arnaud Vandaele

The alternating direction method of multipliers (ADM or ADMM) breaks a complex optimization problem into much simpler subproblems. The ADM algorithms are typically short and easy to implement yet exhibit (nearly) state-of-the-art…

Optimization and Control · Mathematics 2021-02-02 Ming Yan , Wotao Yin

The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of…

Optimization and Control · Mathematics 2024-02-08 Rina Foygel Barber , Emil Y. Sidky

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…

Optimization and Control · Mathematics 2015-05-20 Robert Nishihara , Laurent Lessard , Benjamin Recht , Andrew Packard , Michael I. Jordan

In this paper, we develop a dual alternating direction method of multipliers (ADMM) for an image decomposition model. In this model, an image is divided into two meaningful components, i.e., a cartoon part and a texture part. The…

Image and Video Processing · Electrical Eng. & Systems 2024-12-20 Qingsong Wang , Chengjing Wang , Peipei Tang , Dunbiao Niu

We expand the scope of the alternating direction method of multipliers (ADMM). Specifically, we show that ADMM, when employed to solve problems with multiaffine constraints that satisfy certain verifiable assumptions, converges to the set…

Optimization and Control · Mathematics 2019-10-24 Wenbo Gao , Donald Goldfarb , Frank E. Curtis

We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints.…

Numerical Analysis · Mathematics 2020-02-13 Martin Benning , Florian Knoll , Carola-Bibiane Schönlieb , Tuomo Valkonen

In recent years, several convergent multi-block variants of the alternating direction method of multipliers (ADMM) have been proposed for solving the convex quadratic semidefinite programming via its dual, which is naturally a 3-block…

Optimization and Control · Mathematics 2018-07-06 Xiaokai Chang , Liang Chen , Sanyang Liu

The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex…

Numerical Analysis · Mathematics 2019-07-02 Jianchao Bai , Junli Liang , Ke Guo , Yang Jing

In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $\phi(x_0,\ldots,x_p,y)$, subject to coupled linear equality…

Optimization and Control · Mathematics 2018-05-31 Yu Wang , Wotao Yin , Jinshan Zeng

We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex problem of finding the distance between the boundaries of…

Optimization and Control · Mathematics 2021-07-06 M. V. Dolgopolik

We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints. Previous analysis of the ADMM typically…

Optimization and Control · Mathematics 2013-03-27 Mingyi Hong , Zhi-Quan Luo

We propose a distributed optimization method for solving a distributed model predictive consensus problem. The goal is to design a distributed controller for a network of dynamical systems to optimize a coupled objective function while…

Optimization and Control · Mathematics 2012-12-07 Tyler H. Summers , John Lygeros

In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…

Optimization and Control · Mathematics 2015-08-11 Deren Han , Defeng Sun , Liwei Zhang

The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the…

Optimization and Control · Mathematics 2016-11-17 Euhanna Ghadimi , André Teixeira , Iman Shames , Mikael Johansson

The alternating direction method of multipliers (ADMM) is a versatile tool for solving a wide range of constrained optimization problems, with differentiable or non-differentiable objective functions. Unfortunately, its performance is…

Machine Learning · Computer Science 2017-07-20 Zheng Xu , Mario A. T. Figueiredo , Tom Goldstein

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…

Optimization and Control · Mathematics 2015-06-24 Min Li , Defeng Sun , Kim-Chuan Toh

We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning…

Optimization and Control · Mathematics 2024-11-27 Jiaxiang Li , Shiqian Ma , Tejes Srivastava