# Superlinearly Convergent Asynchronous Distributed Network Newton Method

arXiv: https://arxiv.org/abs/1705.03952 · HTML: https://mlsanity.com/paper/1705.03952/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2017.

## Built on by (most cited first, 1 of 1)

- [Distributed saddle point problems for strongly concave-convex functions](https://mlsanity.com/paper/2202.05812/) (2022)

## Abstract (arXiv)

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on development of fast distributed algorithms under the presence of a central clock. The only known algorithms with convergence guarantees for this problem in asynchronous setup could achieve either sublinear rate under totally asynchronous setting or linear rate under partially asynchronous setting (with bounded delay). In this work, we built upon existing literature to develop and analyze an asynchronous Newton based approach for solving a penalized version of the problem. We show that this algorithm converges almost surely with global linear rate and local superlinear rate in expectation. Numerical studies confirm superior performance against other existing asynchronous methods.