Ill-Conditioned Linear Inequalities

Adrian Lewis
Professor, Department of Combinatorics and Optimization
University of Waterloo

A linear map is "ill-conditioned" when a relatively small perturbation makes it non-subjective. The "condition number" of the map measures this, and is fundamental in computational techniques for equations involving the map. Renegar recently generalized this theory to linear inequalities and associated interior point methods. Using Robinson's notion of "normed convex processes", I will outline a concise result subsuming Renegar's idea.