论文标题
通过收缩分析分布式和随时间变化的原始二重动力学
Distributed and time-varying primal-dual dynamics via contraction analysis
论文作者
论文摘要
在本说明中，我们提供了使用收缩分析与线性相等约束优化问题相关的原始双重动力学的总体分析。对于该问题的众所周知的标准版本：我们建立在凸度下的融合和在强凸度下的收缩率。然后，对于一个规范的分布式优化问题，我们使用部分合并性来建立其原始偶二动力学的全局指数收敛性。作为一个应用程序，我们为最小二乘问题提出了一个新的分布式求解器，并提供相同的收敛保证。最后，对于集中式和分布式原始二元动力学的时变版本，我们利用它们的合同性质以在其跟踪误差上建立界限。为了支持我们的分析，我们介绍了收缩理论的新成果。
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish convergence under convexity and the contracting rate under strong convexity. Then, for a canonical distributed optimization problem, we use partial contractivity to establish global exponential convergence of its primal-dual dynamics. As an application, we propose a new distributed solver for the least-squares problem with the same convergence guarantees. Finally, for time-varying versions of both centralized and distributed primal-dual dynamics, we exploit their contractive nature to establish bounds on their tracking error. To support our analyses, we introduce novel results on contraction theory.
