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This paper presents a tutorial on the Consensus Alternating Direction Method of Multipliers (Consensus ADMM) for distributed optimization, with a specific focus on applications in multi-robot systems. In this tutorial, we derive the…

Optimization and Control · Mathematics 2024-10-08 Jushan Chen

The alternating direction method of multipliers (ADMM) is a powerful algorithm for solving decentralized optimization problems including networked microgrid energy management (NetMEM). However, its performance is highly sensitive to the…

Systems and Control · Electrical Eng. & Systems 2025-11-13 Jesus Silva-Rodriguez , Xingpeng Li

To meet the ever growing demand for both high throughput and uniform coverage in future wireless networks, dense network deployment will be ubiquitous, for which co- operation among the access points is critical. Considering the…

Information Theory · Computer Science 2014-05-14 Yuanming Shi , Jun Zhang , Khaled B. Letaief

As problems in machine learning, smartgrid dispatch, and IoT coordination problems have grown, distributed and fully-decentralized optimization models have gained attention for providing computational scalability to optimization tools.…

Optimization and Control · Mathematics 2018-05-30 Eric Munsing , Scott Moura

In this paper, we show that for a class of linearly constrained convex composite optimization problems, an (inexact) symmetric Gauss-Seidel based majorized multi-block proximal alternating direction method of multipliers (ADMM) is…

Optimization and Control · Mathematics 2019-01-29 Liang Chen , Xudong Li , Defeng Sun , Kim-Chuan Toh

In this paper, we establish the convergence of the proximal alternating direction method of multipliers (ADMM) and block coordinate descent (BCD) for nonseparable minimization models with quadratic coupling terms. The novel convergence…

Optimization and Control · Mathematics 2017-03-16 Caihua Chen , Min Li , Xin Liu , Yinyu Ye

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

We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differential equation (PDE)-constrained optimization problems, where…

Optimization and Control · Mathematics 2024-07-30 Yongcun Song , Xiaoming Yuan , Hangrui Yue

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

Optimization and Control · Mathematics 2015-11-18 Canyi Lu , Huan Li , Zhouchen Lin , Shuicheng Yan

The alternating direction method of multipliers (ADMM) is a most widely used optimization scheme for solving linearly constrained separable convex optimization problems. The convergence of the ADMM can be guaranteed when the dual step…

Optimization and Control · Mathematics 2020-06-23 Guoyong Gu , Junfeng Yang

We present a framework of elastic locomotion, which allows users to enliven an elastic body to produce interesting locomotion by prescribing its high-level kinematics. We formulate this problem as an inverse simulation problem and seek the…

Graphics · Computer Science 2024-05-24 Siyuan Shen , Tianjia Shao , Kun Zhou , Chenfanfu Jiang , Sheldon Andrews , Victor Zordan , Yin Yang

This paper develops a scalable new algorithm, called NysADMM, to minimize a smooth convex loss function with a convex regularizer. NysADMM accelerates the inexact Alternating Direction Method of Multipliers (ADMM) by constructing a…

Optimization and Control · Mathematics 2022-07-05 Shipu Zhao , Zachary Frangella , Madeleine Udell

Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to…

Optimization and Control · Mathematics 2021-11-23 Ziye Liu , Fanghong Guo , Wei Wang , Xiaoqun Wu

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

Alternating direction method of multipliers (ADMM) is a popular optimization tool for the composite and constrained problems in machine learning. However, in many machine learning problems such as black-box attacks and bandit feedback, ADMM…

Optimization and Control · Mathematics 2019-07-31 Feihu Huang , Shangqian Gao , Songcan Chen , Heng Huang

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

This paper presents optimal scaling of the alternating directions method of multipliers (ADMM) algorithm for a class of distributed quadratic programming problems. The scaling corresponds to the ADMM step-size and relaxation parameter, as…

Optimization and Control · Mathematics 2016-11-15 André Teixeira , Euhanna Ghadimi , Iman Shames , Henrik Sandberg , Mikael Johansson

Thanks to its versatility, its simplicity, and its fast convergence, ADMM is among the most widely used approaches for solving a convex problem in distributed form. However, making it running efficiently is an art that requires a fine…

Optimization and Control · Mathematics 2019-07-10 Tomaso Erseghe

The recent deployment of distributed battery units in prosumer premises offer new opportunities for providing aggregated flexibility services to both distribution system operators and balance responsible parties. The optimization problem…

We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…

Optimization and Control · Mathematics 2016-02-23 Musa Maharramov , Stewart A. Levin