Centerpoints: A link between optimization and convex geometry
Optimization and Control
2017-01-19 v3
Abstract
We introduce a concept that generalizes several different notions of a "centerpoint" in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are "best possible" in a certain sense. Motivated by this, we establish several structural results about this concept and provide efficient algorithms for computing these points. Our main motivation is to understand the complexity of oracle based convex mixed-integer optimization.
Cite
@article{arxiv.1511.08609,
title = {Centerpoints: A link between optimization and convex geometry},
author = {Amitabh Basu and Timm Oertel},
journal= {arXiv preprint arXiv:1511.08609},
year = {2017}
}