hyperplane arrangements

Computation of Least Trimmed Squares: A Branch-and-Bound framework with Hyperplane Arrangement Enhancements

  • Xiang Meng
  • Andrés Gómez
  • Rahul Mazumder
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , ,

    We study computational aspects of a key problem in robust statistics—the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large magnitudes. Although statistically attractive, penalized LTS is NP-hard, and existing mixed-integer optimization (MIO) formulations scale poorly due to weak relaxations and … Read more

    Hyperplane Arrangements with Large Average Diameter

  • Antoine Deza
  • Feng Xie
    • Categories Combinatorial Optimization, Polyhedra Tags , ,

    The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed dimension. We give the exact value of the largest possible average diameter for all simple arrangements in … Read more