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Regularized dual gradient distributed method for constrained convex optimization over unbalanced directed graphs

调整双坡度在失衡的指导的图上为抑制凸的优化散布了方法

作     者:Gu, Chuanye Wu, Zhiyou Li, Jueyou 

作者机构:Cutin Univ Dept Math & Stat Perth WA 6845 Australia Chongqing Normal Univ Sch Math Sci Chongqing 400047 Peoples R China 

出 版 物:《NUMERICAL ALGORITHMS》 (数值算法)

年 卷 期:2020年第84卷第1期

页      面:91-115页

核心收录:

学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基  金:NSFC [11501070, 11671362, 11871128] Natural Science Foundation Projection of Chongqing [cstc2017jcyjA0788, cstc2018jcyjAX0172] Science and Technology Research Program of Chongqing Municipal Education Commission [KJQN201800520] 

主  题:Convex optimization Distributed algorithm Dual decomposition Regularization Multi-agent network 

摘      要:This paper investigates a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subjected to global coupled constraints. Based on push-sum protocol and dual decomposition, we design a regularized dual gradient distributed algorithm to solve this problem, in which the algorithm is implemented in unbalanced time-varying directed graphs only requiring the column stochasticity of communication matrices. By augmenting the corresponding Lagrangian function with a quadratic regularization term, we first obtain the bound of the Lagrangian multipliers which does not require constructing a compact set containing the dual optimal set when compared with most of primal-dual based methods. Then, we obtain that the convergence rate of the proposed method can achieve the order of O(lnT/T) for strongly convex objective functions, where T is the number of iterations. Moreover, the explicit bound of constraint violations is also given. Finally, numerical results on the network utility maximum problem are used to demonstrate the efficiency of the proposed algorithm.

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