论文标题
通过新颖的分布式算法解决非平滑资源分配问题以及可行性约束
Solving Nonsmooth Resource Allocation Problems with Feasibility Constraints through Novel Distributed Algorithms
论文作者
论文摘要
本文研究了多代理网络上的分布式非平滑资源分配问题，在本文中，每个代理都受到全球耦合网络资源约束的约束，并且在一般凸集集中所描述的局部可行性约束。为了解决此类问题，提出了两类通过差分包含和投影算子的新型分布式连续算法。此外，通过Lyapunov功能理论和非平滑分析来分析算法的收敛性。我们说明，当相互作用的挖掘量是重量平衡并且局部成本功能强烈凸出时，第一种算法可以全球范围融合到问题的确切最佳问题。此外，研究算法的完全分布式实现在具有严格凸出局部成本函数的连接的无向图上进行了研究。此外，为了改善需要初始化的第一种算法的缺点，我们设计了第二个算法，可以在没有初始化的情况下实现，以实现与具有强大凸成本功能的连接的无向图上的最佳解决方案的全局收敛。最后，几个数值模拟验证了结果。
The distributed non-smooth resource allocation problem over multi-agent networks is studied in this paper, where each agent is subject to globally coupled network resource constraints and local feasibility constraints described in terms of general convex sets. To solve such a problem, two classes of novel distributed continuous-time algorithms via differential inclusions and projection operators are proposed. Moreover, the convergence of the algorithms is analyzed by the Lyapunov functional theory and nonsmooth analysis. We illustrate that the first algorithm can globally converge to the exact optimum of the problem when the interaction digraph is weight-balanced and the local cost functions being strongly convex. Furthermore, the fully distributed implementation of the algorithm is studied over connected undirected graphs with strictly convex local cost functions. In addition, to improve the drawback of the first algorithm that requires initialization, we design the second algorithm which can be implemented without initialization to achieve global convergence to the optimal solution over connected undirected graphs with strongly convex cost functions. Finally, several numerical simulations verify the results.
