Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks

In this paper, we focus on the nonsmooth composite optimization problems over networks, which consist of a smooth term and a nonsmooth term. Both equality constraints and box constraints for the decision variables are also considered. Based on the multi-agent networks, the objective problems are spl...

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Main Authors: Liping Feng, Liang Ran, Guoyang Meng, Jialong Tang, Wentao Ding, Huaqing Li
Format: Article
Language:English
Published: MDPI AG 2022-09-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/24/9/1278
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author Liping Feng
Liang Ran
Guoyang Meng
Jialong Tang
Wentao Ding
Huaqing Li
author_facet Liping Feng
Liang Ran
Guoyang Meng
Jialong Tang
Wentao Ding
Huaqing Li
author_sort Liping Feng
collection DOAJ
description In this paper, we focus on the nonsmooth composite optimization problems over networks, which consist of a smooth term and a nonsmooth term. Both equality constraints and box constraints for the decision variables are also considered. Based on the multi-agent networks, the objective problems are split into a series of agents on which the problems can be solved in a decentralized manner. By establishing the Lagrange function of the problems, the first-order optimal condition is obtained in the primal-dual domain. Then, we propose a decentralized algorithm with the proximal operators. The proposed algorithm has uncoordinated stepsizes with respect to agents or edges, where no global parameters are involved. By constructing the compact form of the algorithm with operators, we complete the convergence analysis with the fixed-point theory. With the constrained quadratic programming problem, simulations verify the effectiveness of the proposed algorithm.
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spelling doaj.art-cf11d73cc08b4d8186f7428f8da9b6d02023-11-23T16:08:58ZengMDPI AGEntropy1099-43002022-09-01249127810.3390/e24091278Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over NetworksLiping Feng0Liang Ran1Guoyang Meng2Jialong Tang3Wentao Ding4Huaqing Li5Department of Computer Science, Xinzhou Teachers University, Xinzhou 034000, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaDepartment of Mathematics, Xinzhou Teachers University, Xinzhou 034000, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaDepartment of Computer Science, Xinzhou Teachers University, Xinzhou 034000, ChinaIn this paper, we focus on the nonsmooth composite optimization problems over networks, which consist of a smooth term and a nonsmooth term. Both equality constraints and box constraints for the decision variables are also considered. Based on the multi-agent networks, the objective problems are split into a series of agents on which the problems can be solved in a decentralized manner. By establishing the Lagrange function of the problems, the first-order optimal condition is obtained in the primal-dual domain. Then, we propose a decentralized algorithm with the proximal operators. The proposed algorithm has uncoordinated stepsizes with respect to agents or edges, where no global parameters are involved. By constructing the compact form of the algorithm with operators, we complete the convergence analysis with the fixed-point theory. With the constrained quadratic programming problem, simulations verify the effectiveness of the proposed algorithm.https://www.mdpi.com/1099-4300/24/9/1278nonsmooth optimizationdecentralized optimizationprimal-dual algorithmuncoordinated stepsizesdistributed signal processinginformation processing
spellingShingle Liping Feng
Liang Ran
Guoyang Meng
Jialong Tang
Wentao Ding
Huaqing Li
Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks
Entropy
nonsmooth optimization
decentralized optimization
primal-dual algorithm
uncoordinated stepsizes
distributed signal processing
information processing
title Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks
title_full Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks
title_fullStr Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks
title_full_unstemmed Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks
title_short Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks
title_sort decentralized primal dual proximal operator algorithm for constrained nonsmooth composite optimization problems over networks
topic nonsmooth optimization
decentralized optimization
primal-dual algorithm
uncoordinated stepsizes
distributed signal processing
information processing
url https://www.mdpi.com/1099-4300/24/9/1278
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AT liangran decentralizedprimaldualproximaloperatoralgorithmforconstrainednonsmoothcompositeoptimizationproblemsovernetworks
AT guoyangmeng decentralizedprimaldualproximaloperatoralgorithmforconstrainednonsmoothcompositeoptimizationproblemsovernetworks
AT jialongtang decentralizedprimaldualproximaloperatoralgorithmforconstrainednonsmoothcompositeoptimizationproblemsovernetworks
AT wentaoding decentralizedprimaldualproximaloperatoralgorithmforconstrainednonsmoothcompositeoptimizationproblemsovernetworks
AT huaqingli decentralizedprimaldualproximaloperatoralgorithmforconstrainednonsmoothcompositeoptimizationproblemsovernetworks