In this paper, we study the problem of minimizing a sum of convex objective functions, which are locally available to agents in a network. Distributed optimization algorithms make it possible for the agents to cooperatively solve the problem through local computations and communications with neighbors. Lagrangian-based distributed optimization algorithms have received significant attention in recent years, due to their exact convergence property. However, many of these algorithms have slow convergence or are expensive to execute. In this paper, we propose a flexible framework of first-order primal-dual algorithms (FlexPD), which allows for an arbitrary number of primal steps per iteration. This framework includes three algorithms, FlexPD-F, FlexPD-G, and FlexPD-C that can be customized for various applications with different computation and communication requirements. For strongly convex and Lipschitz gradient objective functions, by carefully controlling the stepsize choices, we establish linear convergence of our proposed framework to the optimal solution. Simulation results confirm the superior performance of our framework compared to the existing methods.

中文翻译：

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FlexPD：用于分布式优化的一阶原始对偶算法的灵活框架


在本文中，我们研究了最小化凸目标函数之和的问题，这些函数对于网络中的代理来说是本地可用的。分布式优化算法使智能体能够通过本地计算和与邻居的通信来协作解决问题。基于拉格朗日的分布式优化算法由于其精确的收敛性，近年来受到了广泛的关注。然而，许多这些算法收敛速度慢或者执行成本昂贵。在本文中，我们提出了一种灵活的一阶原始对偶算法（FlexPD）框架，它允许每次迭代使用任意数量的原始步骤。该框架包括 FlexPD-F、FlexPD-G 和 FlexPD-C 三种算法，可以针对具有不同计算和通信要求的各种应用进行定制。对于强凸和 Lipschitz 梯度目标函数，通过仔细控制步长选择，我们建立了我们提出的框架到最佳解决方案的线性收敛。仿真结果证实了我们的框架比现有方法具有优越的性能。