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Regularized dual gradient distributed method for constrained convex optimization over unbalanced directed graphs
Numerical Algorithms ( IF 2.1 ) Pub Date : 2019-06-14 , DOI: 10.1007/s11075-019-00746-2
Chuanye Gu , Zhiyou Wu , Jueyou Li

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 \(\mathcal {O}(\ln T/T)\) 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.



中文翻译:

不平衡有向图约束凸优化的正则化双梯度分布方法

本文研究了协作多智能体时变网络上的分布式优化问题,其中每个智能体都有自己的决策变量,应该对其进行设置,以使其在全局耦合约束下的个体目标最小化。基于推和和协议和对偶分解,我们设计了一种正则化对偶梯度分布算法来解决此问题,该算法在不平衡时间中实现–改变有向图只需要通信矩阵的列随机性即可。通过用二次正则项扩展相应的拉格朗日函数,我们首先获得了拉格朗日乘数的界线,与大多数基于偶对偶的方法相比,该界线无需构造包含对偶最优集的紧凑集。然后,\(\ mathcal {O}(\ ln T / T)\)用于强凸目标函数,其中T是迭代次数。此外,还给出了违反约束的明确界限。最后,利用网络效用最大问题的数值结果证明了该算法的有效性。

更新日期:2020-04-22
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