This paper studies a nonsmooth resource allocation problem with network resource constraints and local set constraints, where the interaction graphs among agents are generally strongly connected digraphs. First, we design a centralized continuous-time proximal gradient algorithm, where each agent uses the global Lagrangian multipliers and the global values of constraint functions. For the case that the agents' private information could not be leaked and the global Lagrangian multipliers are not available, the agents are endowed with some additional variables to estimate those global information via consensus protocols. Then, we construct a class of continuous-time distributed proximal gradient algorithms by using a two-time scale mechanism to integrate the proposed proximal gradient algorithm and consensus protocols. By adopting Lyapunov stability theory and convex optimization theory, we prove that the decision variables asymptotically converge to the optimal solution of the nonsmooth resource allocation problem. Finally, numerical simulations are applied to illustrate the effectiveness of the proposed algorithms.

中文翻译：

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一般有向图上非平滑资源分配的连续时间分布式近似梯度算法


本文研究了具有网络资源约束和局部集约束的非光滑资源分配问题，其中智能体之间的交互图通常是强连通有向图。首先，我们设计了一种集中式连续时间近端梯度算法，其中每个智能体使用全局拉格朗日乘子和约束函数的全局值。对于代理的私人信息不能泄露且全局拉格朗日乘数不可用的情况，赋予代理一些额外的变量，通过共识协议来估计这些全局信息。然后，我们通过使用两倍尺度机制来集成所提出的近端梯度算法和共识协议，构建一类连续时间分布式近端梯度算法。采用Lyapunov稳定性理论和凸优化理论，证明决策变量渐近收敛于非光滑资源分配问题的最优解。最后，通过数值模拟来说明所提出算法的有效性。