论文标题
凸的算法降低：在更高维度中的分布式合成和有限时间终止
Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension
论文作者
论文摘要
我们介绍了一个通用的数学框架，用于分布式算法，并在应用程序中经常满足单调性属性。这些属性具有杠杆作用，以提供有限的时间保证，用于融合算法，该算法适用于没有中央当局。中心应用是在更高维度的共识算法中。这些追求激发了新的同伴对等凸赫尔算法的同行，我们证明这是描述理论的实例化。为了解决凸集的多样性以及在高维度中了解此类集合的潜在计算和通信成本，开发了基于标准的轻质标准。更明确地，我们给出了一种分布式算法，该算法将在更高维度的共识问题应用于有限的时间内终止，并保证在任何给定的公差内，在常规中的共识算法的收敛。开发了最小二乘估计和分布式功能确定的应用。通过MATLAB模拟说明了算法的实际效用。
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited for use in the absence of a central authority. A central application is to consensus algorithms in higher dimension. These pursuits motivate a new peer to peer convex hull algorithm which we demonstrate to be an instantiation of the described theory. To address the diversity of convex sets and the potential computation and communication costs of knowing such sets in high dimension, a lightweight norm based stopping criteria is developed. More explicitly, we give a distributed algorithm that terminates in finite time when applied to consensus problems in higher dimensions and guarantees the convergence of the consensus algorithm in norm, within any given tolerance. Applications to consensus least squared estimation and distributed function determination are developed. The practical utility of the algorithm is illustrated through MATLAB simulations.
