The Mixing Time of the Dikin Walk in a Polytope - A Simple Proof
Data Structures and Algorithms
2016-08-10 v2 Optimization and Control
Abstract
We study the mixing time of the Dikin walk in a polytope - a random walk based on the log-barrier from the interior point method literature. This walk, and a close variant, were studied by Narayanan (2016) and Kannan-Narayanan (2012). Bounds on its mixing time are important for algorithms for sampling and optimization over polytopes. Here, we provide a simple proof of their result that this random walk mixes in time O(mn) for an n-dimensional polytope described using m inequalities.
Cite
@article{arxiv.1508.01977,
title = {The Mixing Time of the Dikin Walk in a Polytope - A Simple Proof},
author = {Sushant Sachdeva and Nisheeth K. Vishnoi},
journal= {arXiv preprint arXiv:1508.01977},
year = {2016}
}
Comments
5 pages, published in Operations Research Letters