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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

This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a…

Optimization and Control · Mathematics 2020-06-09 Liang Chen , Defeng Sun , Kim-Chuan Toh

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

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

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

Optimization and Control · Mathematics 2026-05-04 Leandro Farias Maia , David H. Gutman , Renato D. C. Monteiro , Gilson N. Silva

In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…

Optimization and Control · Mathematics 2023-10-11 Qinian Jin

We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design…

Optimization and Control · Mathematics 2025-09-25 Harsh Choudhary , Sven Leyffer , Dominic Yang

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

In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced…

Optimization and Control · Mathematics 2017-07-27 Feihu Huang , Songcan Chen , Zhaosong Lu

In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate…

Optimization and Control · Mathematics 2018-01-17 Yunhai Xiao , Liang Chen , Donghui Li

We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both…

Optimization and Control · Mathematics 2014-09-15 Huahua Wang , Arindam Banerjee , Zhi-Quan Luo

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…

Machine Learning · Computer Science 2013-08-19 Leon Wenliang Zhong , James T. Kwok

Stochastic alternating direction method of multipliers (SADMM) is a popular method for solving nonconvex nonsmooth optimization in various applications. However, it typically requires an empirical selection of the static batch size for…

Optimization and Control · Mathematics 2026-01-23 Jiachen Jin , Kangkang Deng , Boyu Wang , Hongxia Wang

We study a class of structured convex optimization problems, which have a two-block separable objective and nonlinear functional constraints as well as affine constraints that couple the two block variables. Such problems naturally arise…

Optimization and Control · Mathematics 2026-02-27 Zhengjie Xiong , Yangyang Xu

The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems. In particular, the ADMM can solve convex programs that minimize the sum of $N$ convex functions with $N$-block…

Optimization and Control · Mathematics 2015-05-26 Tianyi Lin , Shiqian Ma , Shuzhong Zhang

In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with \emph{nonlinear coupling constraints}. Distinctive features of our proposed method,…

Optimization and Control · Mathematics 2024-02-22 Le Thi Khanh Hien , Dimitri Papadimitriou

The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and…

Optimization and Control · Mathematics 2021-07-15 Bingsheng He , Shengjie Xu , Xiaoming Yuan

This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…

Optimization and Control · Mathematics 2018-05-21 Vando A. Adona , Max L. N. Goncalves , Jefferson G. Melo

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