论文标题
在不平衡的有向网络上进行非convex优化的完全分布的连续时间算法
Fully Distributed Continuous-Time Algorithm for Nonconvex Optimization over Unbalanced Directed Networks
论文作者
论文摘要
本文研究了不平衡的定向网络，研究了分布式连续的非凸优化问题。目的是合作将所有代理商陈述到最佳解决方案，以最大程度地减少当地成本功能的总和。基于拓扑平衡技术和自适应控制方法，为每个代理开发了一种新颖的完全分布式算法，并且既没有有关网络连接性的全局信息，也不是本地成本函数的凸性。通过将所提出的算法视为一种扰动系统，首先建立了其输入到状态的稳定性，其输入到状态的稳定性首先建立，并且在放松条件下，决策变量对最佳解决方案的渐近收敛性被证明。该算法设计的一个关键特征是，它消除了对局部成本函数最小的强凸常数的依赖性，而左侧特征向量对应于不平衡的定向拓扑的Laplacian矩阵的零特征值。用两个示例说明了所提出的完全分布算法的有效性。
This paper investigates the distributed continuous-time nonconvex optimization problem over unbalanced directed networks. The objective is to cooperatively drive all the agent states to an optimal solution that minimizes the sum of the local cost functions. Based on the topology balancing technique and adaptive control approach, a novel fully distributed algorithm is developed for each agent with neither prior global information concerning network connectivity nor convexity of local cost functions. By viewing the proposed algorithm as a perturbed system, its input-to-state stability with a vanishing perturbation is first established, and asymptotic convergence of the decision variables toward the optimal solution is then proved under the relaxed condition. A key feature of the algorithm design is that it removes the dependence on the smallest strong convexity constant of local cost functions, and the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix of unbalanced directed topologies. The effectiveness of the proposed fully distributed algorithm is illustrated with two examples.
