论文标题
在有导网络中的二重性分布式优化
Bilevel Distributed Optimization in Directed Networks
论文作者
论文摘要
由无线传感器网络中的新兴应用程序和大规模数据处理的激励，我们考虑在有向网络上进行优化，在这些网络中，代理商在本地向邻居传达其信息以合作将全球成本函数最小化。我们介绍了一个新的统一分布式约束优化模型，该模型被描述为双重优化问题。该模型捕获了有针对性网络的各种现有问题，包括：（i）具有线性约束的分布式优化； （ii）在有向网络上分布了无约束的无限凸优化。采用新型的基于正则化的松弛方法和梯度跟踪方案，我们开发了一种迭代的正则化推力梯度算法。我们建立了共识，并得出了新的收敛速率声明，以实现生成的迭代次数的次级优势和不可见性，以解决二聚体模型。这项工作中获得的算法和复杂性分析似乎是解决双重模型以及两个问题子类的新事物。提出了所提出算法的数值性能。
Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to cooperatively minimize a global cost function. We introduce a new unifying distributed constrained optimization model that is characterized as a bilevel optimization problem. This model captures a wide range of existing problems over directed networks including: (i) Distributed optimization with linear constraints; (ii) Distributed unconstrained nonstrongly convex optimization over directed networks. Employing a novel regularization-based relaxation approach and gradient-tracking schemes, we develop an iteratively regularized push-pull gradient algorithm. We establish the consensus and derive new convergence rate statements for suboptimality and infeasibility of the generated iterates for solving the bilevel model. The proposed algorithm and the complexity analysis obtained in this work appear to be new for addressing the bilevel model and also for the two sub-classes of problems. The numerical performance of the proposed algorithm is presented.
