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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Bibliographic Details
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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Summary: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.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2021.3110295