论文标题
通过分布式流畅的多速度算法来解决一类非滑动资源分配问题
Solving A Class of Nonsmooth Resource Allocation Problems with Directed Graphs though Distributed Smooth Multi-Proximal Algorithms
论文作者
论文摘要
在本文中，提出了两种分布式的多二个原始二偶有算法来处理一类分布式非平滑资源分配问题。在这些问题中，全局成本函数是局部凸和非平滑成本函数的总和，每个函数都由一个两倍的可区分函数和多个非滑动功能组成。底座多代理系统的通信图是指向和密切相关的，但不一定是加权平衡。多型拆分旨在应对这些非平滑函数的求和的难以及格属性所造成的困难。此外，它还可以保证提出的算法的平滑度。引入了多轴向分裂中的辅助变量以估算非平滑函数的亚级别。从理论上讲，收敛分析是通过采用Lyapunov稳定性理论和相对于集合的积分输入对国家稳定性（IISS）理论进行的。它表明，提出的算法可以使状态融合到满足资源分配条件的最佳点。
In this paper, two distributed multi-proximal primal-dual algorithms are proposed to deal with a class of distributed nonsmooth resource allocation problems. In these problems, the global cost function is the summation of local convex and nonsmooth cost functions, each of which consists of one twice differentiable function and multiple nonsmooth functions. Communication graphs of underling multi-agent systems are directed and strongly connected but not necessarily weighted-balanced. The multi-proximal splitting is designed to deal with the difficulty caused by the unproximable property of the summation of those nonsmooth functions. Moreover, it can also guarantee the smoothness of proposed algorithms. Auxiliary variables in the multi-proximal splitting are introduced to estimate subgradients of nonsmooth functions. Theoretically, the convergence analysis is conducted by employing Lyapunov stability theory and integral input-to-state stability (iISS) theory with respect to set. It shows that proposed algorithms can make states converge to the optimal point that satisfies resource allocation conditions.
