Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users...
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Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users' constraint sets, where each user has its own private nonsmoothconvex objective function and closed convex constraint set, which is the intersection of a number of simple, closed convex sets. One algorithm enables each user to adjust its estimate using the proximity operator of its objective function and the metric projection onto one constraint set randomly selected from a number of simple, closed convex sets. The other determines each user's estimate using the subdifferential of its objective function instead of the proximity operator. Investigation of the two algorithms' convergence properties for a diminishing step-size rule revealed that, under certain assumptions, the sequences of all users generated by each of the two algorithms converge almost surely to the same solution. It also showed that the rate of convergence depends on the step size and that a smaller step size results in quicker convergence. The results of numerical evaluation using a nonsmoothconvexoptimization problem support the convergence analysis and demonstrate the effectiveness of the two algorithms.
作者：
Zeng, XianlinLiang, ShuChen, JieBeijing Inst Technol
Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Univ Sci & Technol Beijing
Sch Automat & Elect Engn Minist Educ Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Beijing Inst Technol
Minist Educ Beijing Adv Innovat Ctr Intelligent Robots & Syst Key Lab Biomimet Robots & Syst Beijing 100081 Peoples R China
In this paper, we investigate a privacy preservation design in the distributed nonsmooth convex optimization with set constraints. To solve the distributedoptimization problem while preserving the privacy, we use pse...
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ISBN:
(纸本)9789881563958
In this paper, we investigate a privacy preservation design in the distributed nonsmooth convex optimization with set constraints. To solve the distributedoptimization problem while preserving the privacy, we use pseudo-subgradients involved with (non-integrable) set-valued functions. Based on pseudo-subgradients, we propose distributednonsmoothoptimization algorithms with keeping subgradient information confidential. Then we prove the correctness and convergence of the distributed privacy preservation optimization algorithms to achieve the exact solution of the original optimization problem.
In this paper, we investigate a privacy preservation design in the distributed nonsmooth convex optimization with set constraints. To solve the distributedoptimization problem while preserving the privacy, we use pse...
详细信息
In this paper, we investigate a privacy preservation design in the distributed nonsmooth convex optimization with set constraints. To solve the distributedoptimization problem while preserving the privacy, we use pseudo-subgradients involved with（non-integrable） set-valued functions. Based on pseudo-subgradients, we propose distributednonsmoothoptimization algorithms with keeping subgradient information confidential. Then we prove the correctness and convergence of the distributed privacy preservation optimization algorithms to achieve the exact solution of the original optimization problem.
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