Primal-Dual Fixed Point Algorithms Based on Adapted Metric for Distributed Optimization

This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed prim...

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Published in:	IEEE transaction on neural networks and learning systems Vol. 34; no. 6; pp. 2923 - 2937
Main Authors:	Li, Huaqing, Zheng, Zuqing, Lu, Qingguo, Wang, Zheng, Gao, Lan, Wu, Guo-Cheng, Ji, Lianghao, Wang, Huiwei
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.06.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Adapted metric method Algorithms Approximation algorithms completely distributed Convergence Convex functions Fixed points (mathematics) Iterative methods Linear operators Mathematical analysis Mathematical models Measurement nonsmooth convex function Operators (mathematics) Optimization Prediction algorithms primal–dual fixed point algorithm randomized asynchronous iterative Signal processing algorithms
ISSN:	2162-237X, 2162-2388, 2162-2388
Online Access:	Get full text
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Abstract	This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.
AbstractList	This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results. This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.
Author	Lu, Qingguo Zheng, Zuqing Li, Huaqing Gao, Lan Wang, Zheng Wu, Guo-Cheng Ji, Lianghao Wang, Huiwei
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SubjectTerms	Adapted metric method Algorithms Approximation algorithms completely distributed Convergence Convex functions Fixed points (mathematics) Iterative methods Linear operators Mathematical analysis Mathematical models Measurement nonsmooth convex function Operators (mathematics) Optimization Prediction algorithms primal–dual fixed point algorithm randomized asynchronous iterative Signal processing algorithms
Title	Primal-Dual Fixed Point Algorithms Based on Adapted Metric for Distributed Optimization
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