论文标题
加速分布式的投影梯度下降，以通过三重耦合约束来优化凸优化
Accelerated Distributed Projected Gradient Descent for Convex Optimization with Clique-wise Coupled Constraints
论文作者
论文摘要
本文通过一类耦合约束的分布式凸优化问题解决了该问题，该问题是由由集团建模的多个社区组成的多代理系统。首先，我们提出了一种完全分布的基于梯度的算法，其新型操作员受到凸投影的启发，称为基于集团的投影。接下来，我们仔细检查了降低和固定步骤尺寸的收敛属性。对于减小的，我们在目标函数的平滑度和约束集的紧凑性的假设下显示了融合到最佳解决方案。另外，当目标函数强烈单调时，就证明了与独特解决方案的严格收敛性，而无需假设紧凑。对于固定步骤尺寸，我们证明了O（1/K）的非共收敛速率，该量涉及目标函数平稳性的客观残差。此外，我们将Nesterov的加速度方法应用于拟议的算法，并建立O（1/K^2）的收敛速率。数值实验说明了提出的方法的有效性。
This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed gradient-based algorithm with a novel operator inspired by the convex projection, called the clique-based projection. Next, we scrutinize the convergence properties for both diminishing and fixed step sizes. For diminishing ones, we show the convergence to an optimal solution under the assumptions of the smoothness of an objective function and the compactness of the constraint set. Additionally, when the objective function is strongly monotone, the strict convergence to the unique solution is proved without the assumption of compactness. For fixed step sizes, we prove the non-ergodic convergence rate of O(1/k) concerning the objective residual under the assumption of the smoothness of the objective function. Furthermore, we apply Nesterov's acceleration method to the proposed algorithm and establish the convergence rate of O(1/k^2). Numerical experiments illustrate the effectiveness of the proposed method.
