This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal–dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.

中文翻译：

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Primal——基于自适应度量的分布式优化定点算法


本文考虑一组代理在无向网络上的分布式优化。目标是最小化二次可微凸函数和两个可能的非光滑凸函数的总和，其中一个由有界线性算子组成。提出了一种基于自适应度量方法的新型分布式原-对偶不动点算法，该算法利用了可微凸函数的二阶信息。此外，通过结合随机坐标激活机制，我们提出了一种随机异步迭代分布式算法，允许每个代理随机独立地决定是否在每次迭代中执行更新或保持不变，从而减轻通信成本。此外，所提出的算法采用不同的步长来赋予每个代理更多的独立性。数值仿真结果验证了所提算法的可行性和理论结果的正确性。