.png){kind=icon}
返回
Distributed adaptive Newton methods with global superlinear convergence
.png){kind=icon}
OA
AI
DOI：10.1016/j.automatica.2021.110156.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
This paper considers the distributed optimization problem where each node of a peer-to-peer network minimizes a finite sum of objective functions by communicating with its neighboring nodes. In sharp contrast to the existing literature where the fastest distributed algorithms converge either with a global linear or a local superlinear rate, we propose a distributed adaptive Newton (DAN) algorithm with a global quadratic convergence rate. Our key idea lies in the design of a finite-time set-consensus method with Polyak's adaptive stepsize. Moreover, we introduce a low-rank matrix approximation (LA) technique to compress the innovation of Hessian matrix so that each node only needs to transmit message of dimension O(p) (where p is the dimension of decision vectors) per iteration, which is essentially the same as that of first-order methods. Nevertheless, the resulting DAN-LA converges to an optimal solution with a global superlinear rate. Numerical experiments on logistic regression problems are conducted to validate their advantages over existing methods. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.
Keyword:
Distributed optimization
Newton method
Low-rank approximation
Superlinear convergence
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
5.9
论文数:
1.2W
被引数:
5.2W
机构
引用论文
.png){kind=icon}
A distributed and efficient flooding scheme using 1-hop information in mobile ad hoc networks移动ad hoc网络中使用1跳信息的分布式高效泛洪方案
PREAI
分享收藏A Newton Tracking Algorithm With Exact Linear Convergence for Decentralized Consensus OptimizationOAAI
OAAI分享收藏A Decentralized Second-Order Method with Exact Linear Convergence Rate for Consensus OptimizationOAAI
OAAI分享收藏
查看更多内容