Let K be a full-dimensional convex subset of Rn. We describe a new polynomial-time Turing reduction from the weak separation problem for K to the weak optimization problem for K that is based on a geometric heuristic. We compare our reduction, which relies on analytic centers, with the standard, more general reduction.
@article{arxiv.cs/0603089,
title = {Convex Separation from Optimization via Heuristics},
author = {Lawrence M. Ioannou and Benjamin C. Travaglione and Donny Cheung},
journal= {arXiv preprint arXiv:cs/0603089},
year = {2007}
}