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This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rank formulation, which is a generalization of the…

Numerical Analysis · Mathematics 2021-05-10 Peter Benner , Zvonimir Bujanović , Patrick Kürschner , Jens Saak

We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers…

Systems and Control · Electrical Eng. & Systems 2022-09-09 Chuangchuang Sun

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

Optimization and Control · Mathematics 2017-12-07 Ganzhao Yuan , Bernard Ghanem

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

Multi-agent distributed consensus optimization problems arise in many signal processing applications. Recently, the alternating direction method of multipliers (ADMM) has been used for solving this family of problems. ADMM based distributed…

Systems and Control · Computer Science 2015-06-18 Tsung-Hui Chang , Mingyi Hong , Xiangfeng Wang

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

Optimization and Control · Mathematics 2013-09-13 Didier Henrion

Aiming at solving large-scale learning problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the learning problem as a consensus problem, the ADMM can…

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

In this paper, we consider solving multiple-block separable convex minimization problems using alternating direction method of multipliers (ADMM). Motivated by the fact that the existing convergence theory for ADMM is mostly limited to the…

Optimization and Control · Mathematics 2013-08-27 Xiangfeng Wang , Mingyi Hong , Shiqian Ma , Zhi-Quan Luo

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

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with…

Optimization and Control · Mathematics 2016-09-21 Aryan Mokhtari , Wei Shi , Qing Ling , Alejandro Ribeiro

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

We consider a class of distributed optimization problem where the objective function consists of a sum of strongly convex and smooth functions and a (possibly nonsmooth) convex regularizer. A multi-agent network is assumed, where each agent…

Optimization and Control · Mathematics 2021-10-01 Yichuan Li , Yonghai Gong , Nikolaos M. Freris , Petros Voulgaris , Dusan Stipanovic

This work presents stochastic optimization methods targeted at least-squares problems involving Monte Carlo integration. While the most common approach to solving these problems is to apply stochastic gradient descent (SGD) or similar…

Optimization and Control · Mathematics 2018-04-27 Gustavo T. Pfeiffer , Yoichi Sato

Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require…

Optimization and Control · Mathematics 2017-10-26 Junyao Guo , Gabriela Hug , Ozan Tonguz

Although the performance of popular optimization algorithms such as Douglas-Rachford splitting (DRS) and the ADMM is satisfactory in small and well-scaled problems, ill conditioning and problem size pose a severe obstacle to their reliable…

Optimization and Control · Mathematics 2024-04-17 Andreas Themelis , Lorenzo Stella , Panagiotis Patrinos

This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM) for solving convex problem: minimize $\sum_{i=1}^N f_i(x_i)$ subject to $\sum_{i=1}^N A_i x_i=c, x_i\in \mathcal{X}_i$. The…

Optimization and Control · Mathematics 2014-03-20 Wei Deng , Ming-Jun Lai , Zhimin Peng , Wotao Yin

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

Optimization and Control · Mathematics 2018-06-15 Quoc Tran-Dinh , Yuzixuan Zhu

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

Machine Learning · Statistics 2009-06-12 Rahul Mazumder , Trevor Hastie , Rob Tibshirani

This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…

Optimization and Control · Mathematics 2025-09-17 Jonathan Eckstein , Chang Yu

Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a…

Machine Learning · Computer Science 2019-08-06 Yawei Zhao , En Zhu , Xinwang Liu , Chang Tang , Deke Guo , Jianping Yin