集中与分布式牛顿方法用于网络优化及扩展
Centralized and Distributed Newton Methods for Network Optimization and Extensions
AI总结：
本文研究集中与分布式牛顿方法在单商品和多商品网络流问题中的应用，比较了传统方法与最新提案，并探讨了分布式计算系统中的实现及扩展问题。
摘要：
我们考虑牛顿方法用于常见的单商品和多商品网络流问题。尽管问题的维度可能非常大，但如近三十年来所展示的，可以使用共轭梯度法和低维网络操作来实现。我们重新审视这些方法，比较它们与更近期的提案，并描述如何在分布式计算系统中实现。我们还讨论了扩展问题，包括弧收益的处理、线性侧约束及相关特殊结构。
英文摘要：
We consider Newton methods for common types of single commodity and multi-commodity network flow problems. Despite the potentially very large dimension of the problem, they can be implemented using the conjugate gradient method and low-dimensional network operations, as shown nearly thirty years ago. We revisit these methods, compare them to more recent proposals, and describe how they can be implemented in a distributed computing system. We also discuss generalizations, including the treatment of arc gains, linear side constraints, and related special structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
