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In this paper, we propose a unified framework of inexact stochastic Alternating Direction Method of Multipliers (ADMM) for solving nonconvex problems subject to linear constraints, whose objective comprises an average of finite-sum smooth…

Optimization and Control · Mathematics 2024-03-05 Yuxuan Zeng , Jianchao Bai , Shengjia Wang , Zhiguo Wang

By enabling the nodes or agents to solve small-sized subproblems to achieve coordination, distributed algorithms are favored by many networked systems for efficient and scalable computation. While for convex problems, substantial…

Optimization and Control · Mathematics 2022-08-24 Yu Yang , Qing-Shan Jia , Zhanbo Xu , Xiaohong Guan , Costas J. Spanos

This paper aims to study a majorized alternating direction method of multipliers with indefinite proximal terms (iPADMM) for convex composite optimization problems. We show that the majorized iPADMM for 2-block convex optimization problems…

Optimization and Control · Mathematics 2018-02-08 Ning Zhang , Jia Wu , Liwei Zhang

The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…

Optimization and Control · Mathematics 2021-03-17 Junxiang Wang , Liang Zhao

The alternating direction method of multipliers (ADMM) has found widespread use in solving separable convex optimization problems. In this paper, by employing Nesterov extrapolation technique, we propose two families of accelerated…

Optimization and Control · Mathematics 2024-05-13 X. He , N. J. Huang , Y. P. Fang

This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the…

Optimization and Control · Mathematics 2017-11-06 Max L. N. Goncalves , Jefferson G. Melo , Renato D. C. Monteiro

The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…

Information Theory · Computer Science 2014-12-19 Mingyi Hong

The alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems, convex or nonconvex, in many engineering fields. However there is a general lack of theoretical…

Optimization and Control · Mathematics 2015-12-01 Mingyi Hong , Zhi-Quan Luo , Meisam Razaviyayn

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…

Optimization and Control · Mathematics 2026-05-18 Weihua Deng , Haiming Song , Hao Wang , Jinda Yang

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

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

We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate…

Optimization and Control · Mathematics 2014-02-13 Yuyuan Ouyang , Yunmei Chen , Guanghui Lan , Eduardo Pasiliao

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

In this paper, we present a semi-proximal alternating direction method of multipliers (ADMM) for solving $3$-block separable convex minimization problems with the second block in the objective being a strongly convex function and one…

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

In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization problems whose objectives contain coupled functions. Our convergence…

Optimization and Control · Mathematics 2017-01-18 Ying Cui , Xudong Li , Defeng Sun , Kim-Chuan Toh

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…

Numerical Analysis · Mathematics 2017-04-11 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato , Simone Rebegoldi

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…

Optimization and Control · Mathematics 2016-04-12 William W. Hager , Hongchao Zhang

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 widely used in solving structured convex optimization problems due to its superior practical performance. On the theoretical side however, a counterexample was shown in [7]…

Optimization and Control · Mathematics 2015-05-20 Tianyi Lin , Shiqian Ma , Shuzhong Zhang

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

Optimization and Control · Mathematics 2019-01-28 Fred Moolekamp , Peter Melchior