Average-case thresholds for exact regularization of linear programs
Abstract
Small regularizers can preserve linear programming solutions exactly. This paper provides the first average-case analysis of exact regularization: with a standard Gaussian cost vector and fixed constraint set, bounds are established for the probability that exact regularization succeeds as a function of regularization strength. Failure is characterized via the Gaussian measure of inner cones, controlled by novel two-sided bounds on the measure of shifted cones. Results reveal dimension-dependent scaling laws and connect exact regularization of linear programs to their polyhedral geometry via the normal fan and the Gaussian (solid-angle) measure of its cones. Computable bounds are obtained in several canonical settings, including regularized optimal transport. Numerical experiments corroborate the predicted scalings and thresholds.
Cite
@article{arxiv.2510.13083,
title = {Average-case thresholds for exact regularization of linear programs},
author = {Michael P. Friedlander and Sharvaj Kubal and Yaniv Plan and Matthew S. Scott},
journal= {arXiv preprint arXiv:2510.13083},
year = {2025}
}
Comments
25 pages, 4 figures