Centralized and Distributed Newton Methods for Network Optimization and Extensions
Numerical Analysis
2015-07-03 v1 Optimization and Control
Abstract
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.
Cite
@article{arxiv.1507.00702,
title = {Centralized and Distributed Newton Methods for Network Optimization and Extensions},
author = {Dimitri P. Bertsekas},
journal= {arXiv preprint arXiv:1507.00702},
year = {2015}
}