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The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…

Optimization and Control · Mathematics 2023-07-11 Yuxuan Zeng , Zhiguo Wang , Jianchao Bai , Xiaojing Shen

Accompanied with the rising popularity of compressed sensing, the Alternating Direction Method of Multipliers (ADMM) has become the most widely used solver for linearly constrained convex problems with separable objectives. In this work, we…

Numerical Analysis · Computer Science 2016-07-12 Canyi Lu , Jiashi Feng , Shuicheng Yan , Zhouchen Lin

We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…

Optimization and Control · Mathematics 2019-12-20 Sebastian Banert , Radu Ioan Bot , Ernö Robert Csetnek

To solve the separable convex optimization problem with linear constraints, Eckstein and Bertsekas introduced the generalized alternating direction method of multipliers (in short, GADMM), which is an efficient and simple acceleration…

Optimization and Control · Mathematics 2022-11-17 Jianwen Peng , Dexi Liu , Xueqing Zhang , Jen-Chih Yao

Alternating Direction Method of Multipliers (ADMM) is a popular method for solving large-scale Machine Learning problems. Stochastic ADMM was proposed to reduce the per iteration computational complexity, which is more suitable for big data…

Numerical Analysis · Computer Science 2023-04-25 Chao Zhang , Zebang Shen , Hui Qian , Tengfei Zhou , Jianya Zhou , Jianying Zhou

In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in [Bai, et al. Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as its linear…

Numerical Analysis · Mathematics 2019-06-20 Jianchao Bai , Xiaokai Chang , Jicheng Li , Fengmin Xu

In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general convex penalty term. When the data is given exactly, we give a…

Numerical Analysis · Mathematics 2016-01-13 Yuling Jiao , Qinian Jin , Xiliang Lu , Weijie Wang

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…

Optimization and Control · Mathematics 2022-03-04 Dinesh Krishnamoorthy , Vyacheslav Kungurtsev

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…

Machine Learning · Computer Science 2015-07-08 Hanie Sedghi , Anima Anandkumar , Edmond Jonckheere

The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…

Optimization and Control · Mathematics 2015-01-16 Hui Zhang , Lizhi Cheng

We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems. Our method is geared toward supervised classification tasks with many examples and features. It…

Machine Learning · Computer Science 2019-07-12 Samy Wu Fung , Sanna Tyrväinen , Lars Ruthotto , Eldad Haber

The alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn towards the ADMM in…

Optimization and Control · Mathematics 2022-08-19 Sedi Bartz , Rubén Campoy , Hung M. Phan

In this paper, we study the local convergence of the standard ADMM scheme for a class of nonconvex composite problems arising from modern imaging and machine learning models. This problem is constrained by a closed convex set, while its…

Optimization and Control · Mathematics 2026-03-24 Xiyuan Xie , Lihua Yang , Qia li

We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic…

Optimization and Control · Mathematics 2024-09-17 M. Marques Alves , M. Geremia

In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our…

Optimization and Control · Mathematics 2023-01-26 Le Thi Khanh Hien , Duy Nhat Phan , Nicolas Gillis

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 aim to accelerate a preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, for solving linearly constrained convex optimization problems. To achieve this,…

Optimization and Control · Mathematics 2024-12-10 Defeng Sun , Yancheng Yuan , Guojun Zhang , Xinyuan Zhao

The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-05-04 Tsung-Hui Chang , Wei-Cheng Liao , Mingyi Hong , Xiangfeng Wang

The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…

Optimization and Control · Mathematics 2022-04-05 Hongwu Li , Haibin Zhang , Yunhai Xiao

We consider the Lasserre hierarchy for computing bounds on the stability number of graphs. The semidefinite programs (SDPs) arising from this hierarchy involve large matrix variables and many linear constraints, which makes them difficult…

Optimization and Control · Mathematics 2025-06-11 Lennart Sinjorgo , Renata Sotirov , Juan C. Vera