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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MDPI AG
2022-09-01
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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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